How long did they wait after applying the Zagg shield before they put on the case? Zagg recomends letting the case sit without using the phone or putting on cases for 12-24 hours. The do this for a couple reasons.
First to let any application liquid that may have gone into the speaker grill or the trackpad dry. If the liquid hasn't dried/evaporated and you turn it on it could cause a short and damge the phone.
Second to let the adhesive that the application liquid activates to cure. Even if you work and work the shield with the included squeegee there will still be some moisture between the shield and the touchscreen. If you don't let the liquid/adhesive cure properly the shield will lift and you will have to reinstall it.
I learned this the hard way, on my second application I let it sit for 12 hours then GENTLY applied the case (black to red gradient snap case). If the silicon case you mentioned doesn't snap on but rather stretches around the edges of the phone, I'd recommend waiting the full 24 hours. That's my experience with Zagg shields. If you don't like the idea of waiting that long, you could try using one of the shields that doesn't require an application liquid (dry with an adhesive) but that will also probably require a curing time, though probably not as long as one with a liquid application process. Just my $.02