OK, in the link you posted, they mention under "Major Features" that this card has TimeShift under the PVR features. This is because you need it for having a PVR.
... (some time later)
Okay, I have done 2 things.
1. I have downloaded the user manual for the product. You can get it from
http://www.avermedia.com/cgi-bin/support_manual.asp . The regular manual is a hell of a lot more useful than the "quick guide" (which is also twice is big as the full manual because all the languages are combined into one document).
2. I have written an e-mail to their tech support and should receive an answer soon.
However, from what I read in the manual, it seems that this product is normally NOT in timeshift mode. Therefore, there should be no lag or any other problems (except for regular lag created by time required for signal to travel along cables, etc.). Searching the manual for the word "time" is quite illuminating.
So, I think you are safe. Or, you can wait for the answer they send me.
EDIT: I have also asked them what kind of lag to expect, so you may want to wait for the answer.