Parece que o escritor de Guerra dos Tronos, Bryan Cogman, já nos respondeu isso. Essencialmente, eles queriam se casar na época e se casar à luz dos Sete, era sua melhor aposta. Ele também alude ao fato de Cat ter sido dos Sete e por isso também desempenhar um papel nisso.

Justin: Why were Robb and Talisa married in the light of the Seven rather than in front of a Heart Tree?

Bryan: Shotgun wedding! Of sorts. They wanted to get married and there was a septon readily available. At any rate, Robb was raised in an interfaith household — he could very well have spent as much time with with Septon Chayle growing up as he did in the godswood. So I don’t see a problem with him having a Seven wedding. But I guess a lot of people do cuz I get asked that question all the time.

Now the line about Karstark praying to the Father in 208… yeah, I should’ve caught that. Karstark would be strictly Old Gods, I think. If it helps, you could read it as “I’d even break my faith and pray to the bloody FATHER if that’s what it took to bring my sons back”… but I’m not sure that was the intent. But maybe it was. I try my best!

_{Winter is Coming, Ask a GoT Writer: Bryan Cogman on the writing process, Robb and Talisa, and Renly’s peach}

Não há muita informação sobre como o casamento foi realizado nos livros:

"I took her castle and she took my heart." Robb smiled. "The Crag was weakly garrisoned, so we took it by storm one night. Black Walder and the Smalljon led scaling parties over the walls, while I broke the main gate with a ram. I took an arrow in the arm just before Ser Rolph yielded us the castle. It seemed nothing at first, but it festered. Jeyne had me taken to her own bed, and she nursed me until the fever passed. And she was with me when the Greatjon brought me the news of . . . of Winterfell. Bran and Rickon." He seemed to have trouble saying his brothers' names. "That night, she . . . she comforted me, Mother."

Catelyn did not need to be told what sort of comfort Jeyne Westerling had offered her son. "And you wed her the next day."

He looked her in the eyes, proud and miserable all at once. "It was the only honorable thing to do. She's gentle and sweet, Mother, she will make me a good wife."
_{Catelyn II, a Storm of Swords}

Não muito mais do que isso é dito sobre isso. A mesma informação que @TheLethalCarrot dá ainda está, não há muitas Weirdwoods no sul, então provavelmente eles pegaram o primeiro septão que encontraram e rolaram com ele.

Jeyne vs Talisa

Essa é uma das poucas diferenças sutis entre o programa e os livros. Os escritores da série mudaram o personagem Jeyne de forma que George R.R. Martin pediu que eles mudassem o nome dela, para evitar confusão:

57 minutes: He talked about how he suggested that the name of the character Robb married in Season 2 be changed to Talisa, given that this was an entirely new character that book readers would not be familiar with (in the novels, Robb's love interest has a different name and history).
_{'Game of Thrones' Season 3 Characters And Scoop From Creator George R.R. Martin}