People have been make the "two turns after contact" suggestion, but as someone who owns both a Blackburn trainer (like the one in the picture) and a CycleOps, I'd say that this may be too tight for the Blackburn.

First, make sure that you use a skewer that fits snugly into the cups and tighten it down well. Then, to adjust the pressure on the tire, I adjust it until it barely makes contact and I tighten it a little (less than 1/4 turn), then grab the wheel and jerk it up and down a bit. If the tire slips on the resistance unit, repeat the process until it doesn't.

As for the change in resistance occuring while you're using it, I've experienced that too (though only with the Blackburn). It usually happens about 3-4 minutes into my session - the resistance will increase and stay at that level for the rest of the session. I asked someone at my LBS about this. He said he's familiar with this feature. He said he doesn't know for sure, but he suspects this feature is built in so the user doesn't have to deal with a higher level of resistance until he is warmed up. Makes sense to me.