I am not sure if this is a Facepunch issue or if it's one of my plugins. But this is happening on both of my servers. When I restart the servers, tugboats seem to "roll back" in a sense where they are in a different location from where they were before the server restarted. Also, some things inside the tugboats, such as boxes, workenches, etc, will just be gone upon server restart. It's weird because nothing else on the server seems to roll back this way. Not sure if I would even call this a roll back but I'm not sure what else to call it. 

You are probably not shutting the server down properly. You should issue the "quit" command and then everything will be saved before shutdown.

I use the "restart" command, the one that quits the server with a timer involved. I would assume this accomplishes the same thing as the "quit" command?

Yes it does. Maybe yout tugs are respawning after restart for some reason?

How would I go about checking to see if that is true?

I don't know if it has anything to do with this but some of them appear under the map and create conflicts in the console. It's as if when they disconnect they go under the water and when they connect they fly out without any sense.