Is it OK to start a PhD with a side project still running from your master's?
Let me answer in two parts:


With the right advisor, projects undertaken on your own initiative will be valued rather than seen as a problem.
You definitely need to talk to your advisor now to make sure you're with the right advisor.


Expanding on this a bit... one of the hardest things for many people to learn in a Ph.D. program is how to organize and initiate their own research portfolio.  You show signs of doing this right from the start, so as long as you are willing to accept feedback and guidance, this is potentially a really good thing.  

Whether it is a good fit for your advisor, however, depends on what your advisor's needs are at their current stage in their career.  Some professors really need their students to be focusing on particular problems that the professor currently wants or needs to tackle.  Others are able to give their students more freedom to wander intellectually.  This is partly based on career stage (pre-tenure professors are likely to demand more focus), and partly on personality (a control freak or an empire-builder will not be mellowed by tenure; a highly confident professor may give much free rein even before tenure).

So: talk with your advisor about your desires and plans.  If your advisor is receptive to the idea, great: now you can sort out how to balance things and make sure you aren't neglecting any responsibilities or making strategic mistakes.  If your advisor is not receptive, you need a different advisor.