2
There are a couple of places you need to check mark in the Groups Admin for your group. They need, Module Access, They Need access to Blocks if any, and they most importantly need Module Admin Access for that module.
Also, if my memory serves me correctly they will not automatically see an admin button like you do as the Webmaster when you log in. They have to click on the module and then the admin link shows up for them in their menu which will allow them access to the modules admin.
HTHs
Quest