No, they're completely independent.
EA has publishing rights for their new IP, but those can be shared if Microsoft pony up the right amount of cash. Importantly it's worth noting the power of exclusivity at the start of a generation. It makes complete sense for Respawn's new IP to be, at least initially (first game), exclusive because they aren't losing many sales from the PS4 (or alternatively Xbox 3) version, yet people are buying their game en masse because of the perceived value of exclusivity.
Perfect example is in your very post. Mass Effect propelled itself to success as a 360 exclusive, and then moved over to other platforms later.
Damn, that Garrus is cute.
Utterly ridiculous.
Wasn't there a clause in the FIFA licensing that meant they had to launch on a certain number of platforms?