Your description, by itself, is too terse to follow easily. Unfortunately, the link seems to be broken -- or at least is coming up empty. You may want to fix that.
From what you said, it appears you're trying to transfer a partially baked red-velvet cake to a partially filled spring form pan in order to serve as a middle layer between layers of unbaked cheesecake batter -- then baking the whole shebang.
I have my doubts about the procedure. Maybe it's just the gloomy disposish of a native pessimist, but I don't see you getting that red-velvet layer out of its own pan without multiple disasters.
The usual method for this sort of madness is to bake the cheesecake layers in separate pans. Cool and freeze them. Bake the red velvet cake layer(s) separately. Allow the red velvet cake to cool, then remove from the pan. Assemble the whole thing with the cheesecake still frozen. Allow to stand until the cheesecake thaws. You may garnish, frost, top or whatever, either before or after the thaw. Exercise your sound discretion in terms of what seems best, all things considered.
If I were making it, I wouldn't use a normal cheesecake crust, but would use a layer of red velvet cake on the bottom instead. My version would go: red velvet - cheese - red velvet - cheese -- frosted top and sides with chantilly cream.
I've done this, but only using a chocolate genoise, never red velvet cake.
PS. You're posting in one of the "professionals only" sections. There's also a general baking thread. Even if you are or were a pro, I suggest asking a moderator to move your post to get more responses.