I have a noob problem and I need your advice.

I bought a new set of strings for my Ibanez RG370dx.
Here are the Strings: Ernie Ball Beefy Slinky Guitar Strings 11's 11 - 54

I managed to set set all the Strings on the guitar but it's very difficult to tune them, because when I tune one, the Bridge rise a little.
When I tune an other one, the bridge rises a little bit more, and untune the first one by the same way, so I have to tune it again, which makes the bridges rises more, and untune the second one, and so on...

I didn't notice this bridge rising before, but when I finally managed pretty much to tune all the 6, the bridge was so rosen I was

I first thought that the strength on the bridge was too high, but it is supposed to handle that for a standard tuning.

I would really appreciate any advices as I'm scared to harm my guitar. The previous string had a smaller gauge. I know that the Strings need so time to set them up but still....

Hope you understood what I said
Thanks for you help.
loosen the the strings. Now tighten the screw in the back of the guitar that hold the springs. You must equalize the tension between the springs and the strings.
Ok I think I found it in the documentation !

It may solve the issue your right !

Thanks a lot.