If the covering was applied wet, and all wrinkles were carefully pulled out, and you made sure the grain was nice and straight, you should have had no problems if the dope you used truly was butyrate. Apply the covering wet, and then dope around the perimiter and allow to dry. Usually, properly-applied silk will be nice and taut. When you apply the dope, the silk may relax a bit, but not so much that it's a problem. It should tighten right up when the dope dries.

After the first 2-3 coats of 50/50 dope/thinner, you should not see any change in the tautness of the covering, although butyrate will tend to continue to shrink over time. That's what can cause surface cracking on old butyrate finishes.

If the covering relaxed, did it come loose when you applied later coats? You do have to be careful that you don't cause the silk to unstick when you start to apply later coats...too much thinner in the dope may cause that to happen. Dope never loses the ability to dissolve itself, so later coats will tend to dissolve earlier coats. If you only have a thin coat around the perimeter holding the silk to the structure, then when you apply later coats, they could loosen the original application you used to stick down the silk. It goes soft, and the silk is now free to move when the dope you apply dries.

Usually, one or two full-strength coats should be applied around the perimeter to prevent this. Now only the uppermost bit of the dope used to stick on the covering will soften, but not enough to cause the silk to loosen.