Welcome, congrats on the new ride!
There are two primary causes for wonky tach behavior on a 900: bad #1 coil and bad tach.
Normally, I would think bad tach, because you said it runs perfect, but I wonder if you're not noticing it running badly below 4k because you're not used to it yet? The most common mode of failure for the coils is running fine above 3-4k, but dropping out below...
Anyway, should be fairly simple to figure out. Pull the lower fairings and get a spray bottle full of water. Start the bike and let it idle for about two minutes. Spray water on each header, and see if one is noticeably colder than the others. If one is cold, that's the one with the bad coil. The tach runs off the #1 coil.
If you know what it sounds like, you can listen and tell if the alternator bolt is broken. If you don't, it's pretty much down to physical inspection.