Got 30mm Scope and 30mm Rings But They Don't Fit?

I got a SS16x and some TPS TSR 30mm rings and the rings seem really tight and by the calipers the ss is 30.08mm and the rings are 29.75mm this causes the scope to sit about a 1/16th inch off the bottom of the rings, do I just push it down? Seems like I might damage something.

You are experiencing "machining tolerance" up front and personal.  On every forum I frequent the pseudo "experts" claim that they don't need to lap or they don't need to check alignment because they have a blah blah blah set of rings and bases and they're perfect so no testing or checking of the alignment of anything is necessary.  BOOO! HISSS!  It just isn't so.  There is nothing in the manufacturing world that is perfect.  There are plus/minus tolerances that apply and a product or part that falls within those tolerances is acceptable, outside of those tolerances is not aceptable.  You just got one component with a minus tolerance and another with a plus tolerance together at the same time.  Those "experts" who claim that rings and bases made by so and so are perfect is talking through a hole in his head.  One can get this exact situation with any manufacturer and you might even get a front ring that's too tight and a rear ring that is too loose.  That's reality. Once shooters figure this out and understand that every single component of a scope installation needs to be checked they will be on the way to obtaining the best accuracy from their firearms.  There are no shortcuts. 

And lapping might void the warranty, call TPS, they'll do you right.

DId you torque the ring bottoms down before you sit the scope in the rings?  If you do that without the caps on it might slightly bend the rings in so the scope will not sit right.  I had that happen with a set of seekins rings.  As soon as I loosened the bottom screws it was all good.  After I got the scope in and the caps torqued I then tightened the bottom screws.