"Partisan bias" is quite rational
The first thing to note is that the size of the shift isn't all that huge. Ten percentage points is politically significant, especially since in a closely divided electorate that shift switches which position has greater support. But it still means that the vast majority of voters would not change their position as a result of hearing party labels.
I also don't think reacting to party labels is necessarily irrational. The platforms are both made up of vague boilerplate. Those of us who follow the immigration debate closely can recognize the shibboleths and infer which specific policy measures they connect to -- but the average poll respondent doesn't have that depth of knowledge. Voters don't formulate preferred policy positions on every issue and then pick the party that will get closest to those positions. Instead, they figure out which party, or which specific leaders, they can trust. A trustworthy party or leader is one who 1) appears knowledgeable and competent with respect to the issue, and 2) appears to care about people like you. If you've come to trust the Republican party to have your interests at heart -- because they share your broader values -- then hearing that a bit of vague boilerplate is Republican vague boilerplate, that's a signal that you can expect that policy to work out in the "right" way when it comes to the specifics of implementation. That's a much easier and more reliable strategy than trying to infer what "comprehensive immigration reform" might actually be.