Hi UB. I have had similar problems. Though, I should add, this problem occurs for me irrespective of Compiz. The only fix I have found to work is to position your right hand top panel icons manually with a little bit more space between them than normal. This seems to stop them dancing around at bootup.
I’m guessing here, but I think the problem may be to do with Mate initially booting with a defualt resolution and then, during login, changing to your preferred resolution that you have previously set up. It is during this resolution changeover that the icons get swapped around. By having the icons a bit more apart from each other, it allows them to remain in the same order for both resolutions.
Edit to add:
I have just taken another look at your desktop snapshot and can see how you have set up your panel and icons centrally with a shortened panel. That being the case, I wonder if you just made your panel a bit longer in order to space your icons out a bit more and also leave a bit of spare panel at each end of the icons, whether that might allow for an unproblematic resolution changeover I was mentioning?