No chronicle of Jaqen's early reign can be explained without first explaining his religion.
It must be noted that at the time Jaqen lived, even after he became Archon of the Step, the Tyroshi didn’t see religion the same way as many throughout Westeros, or even the rest of the Free Cities. There was no established religion. Sure, there was the three-headed god of Trios, which featured on the country’s flag. It had more followers in Tyrosh than any other religion, but was by no means the religious majority in the country. R’hllor has his temples and red priests there as well. Also the moonsingers have their fans in Tyrosh. Even a few Septons wandered the streets in those day, preaching to the heathens. Most every religion currently practiced in the Free Cities, Westeros and the Summer Isles could be found practiced somewhere in Tyrosh. From a business perspective, it helps to keep an open mind about religion. And Tyrosh is a business as much as a country.
Jaqen’s stance on religion made him something of a pariah when he first took residence in Little Tyrosh. He was a practitioner, and a dutiful one at that, of the Faith of the Seven. It was not an unheard of religion, obviously, but certainly not one typically practiced among the Tyroshi elite. Those with status tended to acknowledge Trios as the head diety of the country. Those that knew of Jaqen’s stance on the matter usually treated him with contempt or mild curiosity. It was not a helpful stance to take at the time, so why did Jaqen do it? He was never known as a particularly zealous man, though he actively encouraged his count priests to spread the Faith amongst he smallfolk and was known to be happy to hear of conversions. Within 5 years, most of Little Tyrosh accepted Jaqen’s position on the matter and a majority of the small island worshiped the seven-aspects of the god of the Andals.
What religion Jaqen was raised in is unknown, and what his thoughts were on religion during his time as a sellsword is likewise a mystery. But given his ancestry it’s doubtful he knew much about the Faith before Aegon’s conquest. We do know that, like the rest of Aegon’s court, he acknowledged the faith and pledged himself to the Seven, following his liege’s decision on the matter. The High Septon himself anointed him with oil during his knighting, just as he did for Aegon the Conqueror and Orys Baratheon in their respective conversions. But his own views on the faith were a mystery.
So why is it that Jaqen I would choose the Seven-pointed star to place at his family alter?
It may have been the fact that he was WAS knighted that convinced Jaqen to stick with the faith. Chances are that it was the first public honor he had ever received. And the words he spoke during the knighting ceremony(swearing to be just, protect the innocent, be brave, etc) are not words expected of a sellsword, and Jaqen could have refused the honor. He may have desired the improved status of knighthood. He may have not wanted to refuse such an honor from Aegon I. And he may have been moved by a sense of honor and purpose that until that point in his life, he had lacked. But whatever his reasons for accepting being knighted, by all accounts he did try to live up to them, even when his actions seemed to fly in the face of them. This shows that on some level he still respected the words he had sworn.
But by far the most likely reason for Jaqen remaining with the Faith of the Seven, even after he returned to the Free Cities, was that his wife's own dedication to the Faith. Jaqen honored and acknowledged the Seven. But it was Daella who truly worshiped them. How she came to be so zealous for the Seven is detailed in her journals and letters over a long period of time. Claw Isle was closer in proximity to mainland Westeros than the rest of Aegon’s lands, and was full of smallfolk who worshipped the Seven. She became convinced over the course of her childhood that the one true god was that of the Seven.
Daella often wrote of her wish that Jaqen would convert. It became one of the few qualms she had about accepting his proposal. She felt that marrying a man who did not worship the same gods would be problematic for her. But, having few options within the court of Aegon I, she chose the man who made her the most happy.
The day Daella received word from Jaqen that he had been knighted, and would from that day forward accept her gods as his, nothing is written in her diary other than a few crossed-out scratches and wrinkled parchment indicative of tears. The day after, she could express nothing but joy and wonderment. She had received an answer to a prayer she had been praying for many years. And she wrote of anxious anticipation of seeing her beloved again. The day she did, she wrote these words,
“He looked so HANDSOME. His hair was delightfully green, far brighter than I've ever seen it. It seemed like the dyes he used almost glittered. His new armor was intricate and accentuated his knightly figure. But more than that, he walked stronger, his head was higher, his eyes were more alive than ever before. I asked him how he felt since his knighting. He said he felt no different. But I knew he was changed. He might not have felt it himself, but I knew it. I felt a wanting for him I hadn’t felt since the night he first proposed. If there were ever a moment I would have broken my vows of maidenhood before our marriage, it would have been that moment. Luckily Jaq's sense kicked in before mine did. He said that I would have regretted it afterwards. And he was right. It won't stop me from thinking of that moment tonight, though.”