My location history on Google Maps regularly has me appearing up to half a mile away from where I really am.
The reason for it is that mobiles (and other devices like smart watches) have two methods for working out your location.
The first one is GPS. This is very accurate, but will often lose signal to the satellite, especially if you're indoors. It's also very power intensive, so will drain your battery more quickly. So your phone only usually uses it if it really needs an accurate position, say if you're using a map or fitness app.
The second one is by triangulating your position between 3 phone towers. This is much less power intensive, and will work more reliably. But it is also less accurate. Usually its accurate to a few hundred yards (so a different house on the same street perhaps) but occasionally it'll glitch out completely and put you up to half a mile away. This often happens because it can only find two mobile towers for a minute.
So what you've seen is mostly likely a phone thats been using triangulation, suddenly switching to GPS, or vice versa, and updating the location accordingly.
Completely aside from all that. Nothing good has ever come from tracking someones location this closely @7917Kj . If you don't trust them, then no amount of evidence is going to convince you they're not up to something. Just confront them or end the relationship.