I recently purchased a Nexus 6P (which runs Marshmallow) and have it on Project Fi. I still have my previous phone, a Samsung S3, on Verizon, running on Android 4.4.2 or 3.
I installed Mobilinc on the Nexus and configured it the same as the Samsung phone. The Samsung works fine both local (connected to my home's wi-fi) and remote. I can also connect to the controller remotely using a browser on my work PC (so I know the URL/IP work). The Nexus connects just fine to the controller when local, but it doesn't remotely, wi-fi or cell network.
I do use Tasker for some control tasks. They run fine on the Samsung, not on the Nexus due to the connection problems.
I've tried a variety of things without luck, including playing with the "Aggressive hand off from wi-fi to cell" setting. I vaguely recall this being an issue before, possibly something dealing Mobilinc not handling the transition from Wi-Fi to cell very well, but I don't remember for sure or how it may have been fixed.
Any ideas what I can check? Thanks in advance!