I had a look at this and it doesn't appear to be a bug or badly implemented track indicator. What you are seeing is the accurate magnetic ground track donut. The problem appears to be that the database-provided magnetic variation for the Pine Bluff VOR/DME is incorrect. You are quite correct that the databases say it's 4°E. However, and here's a funny one: the Pine Bluff airport near to the VOR/DME is is declared as 2°E:
Now, as to how the airplane knows its magnetic heading - the IRSes contain a magnetic variation database, which is valid from 2020 through to 2025. The IRS feeds the current date + position and this database computes the actual magnetic variation expected at that position and that's what you're seeing on your avionics. And here's the kicker: the magnetic variation database says the actual magnetic variation should be around 0.3°WEST:
Similar results using the IGRF magnetic model:
You can run the computations for select positions yourself here: https://www.ngdc.noaa.gov/geomag/calculators/magcalc.shtml
Investigating enroute charts, there's a 3 degree declination change over the span of a mere 65 miles. This seem to suggest that the Pine Bluff VOR/DME is misaligned and needs to be realigned IRL:
To summarize: doesn't look like a bug to me. Seems more like either the navaid is misaligned IRL, or the navigational database needs to be updated.