I'm sure I accidentally changed something, but now everything I record is early by an 8th note or so.  After I stop recording and play back all newly recorded audio tracks are early.  I even checked audio recorded from an external synth using a MIDI track that is exactly quantized.  I'm not sure which settings to check.  Any help would be appreciated.
 
Thanks!

Check you are in ASIO mode. All other modes have no way to accurately calculate timing offset. 
 

Definitely in ASIO mode, so that's not it.

OK, what audio interface are you using? 
 
Only place you can change the timing offset is in Preferances/ Audio look at the bottom for manual offset

I have a Steinberg UR22.

This problem appeared for me the first time the other day.

I have not changed anything, I have not installed Windows updates, I have not installed new drivers, nothing. I'm running the latest release of SPLAT on a beefy i7-7700K with 32gb of ram and SSD's.

Also, my problem is opposite of the screen shot you posted. After recording, my audio plays before the MIDI note that triggered it. My audio tracks look like your Tascam US1641 WDM, except the audio is offset before the MIDI note, not after.

Thanks for your help though!

I have a UR44 and have a problem where every now and again recorded audio fails to properly line up with the start and end of the loop points (I always loop record).  When it happens I open preferences and re-apply the driver settings, and then it works properly...for a while.  It is intermittent so sometimes everything is great, and then sometimes I'll lose some really great work.  I am in the process of getting to know Studio One, so it will be interesting to see whether this is a Sonar problem or a Steinberg driver problem that affects other DAWs.   FWIW this started happening sometime in 2017.  I had no such problems 18 months ago - so something definately changed to make this start happening for me. 

UR44 latest drivers, SPLAT lifetime(!) most recent update, Win 7.

I tried reapplying the driver.  It didn't do anything.  I don't understand why this just started happening a day ago when it has not happened before.  You can see the audio track is off-set well before the MIDI note that triggered it.  I'm not recording through plugins or anything.
 

Same computer, same audio interface, same MIDI, same outboard synth recorded in Studio One.  No issues:
 

No one has any advice?

same outboard synth?
 
To perform a loop back test you freeze a VST You can see I used SI drums and a Kick
You run the audio interface output back to an input and re record the sound. Make sure input echo is off on the new audio track. 
 
Your use of an outboard synth would point  a midi driver issue. Not anything to do with your interface unless your using it's midi ports. 
Offset timing is hard to wrap your brain around. 
Your input will be delayed comming in buy the input latency. So the DAW has to play the already recorded tracks ,including midi ahead of time to make up for that. 
 
Your situation is your bypassing your audio output delay and the note is triggered sooner than it is supposed to be played. I'm only guessing. Is the connection to the outboard synth USB or MIDI?