I concur with the above folks that what you describe seems to be normal and fine. Here are some additional thoughts from my experiments and playing around with this stuff myself.
1. Wrap your bucket with a towel/blanket/sleeping bag/etc over the top of your heater. If you're relying on your heater conducting through the bucket wall to heat the beer inside, that same bucket wall is conducting heat out to the environment on the rest of the bucket. Keeping the whole thing insulated keeps things more stable in your fermentor and will help reduce temperature swings/oscillation.
2. Both the Tilt and the Inkbird have the ability to calibrate the temperature sensor. I think of the process really more as an "alignment" rather than a "calibration". People hear the word calibration and get fixated on knowing an exact temperature, and that leads one to an ice bath to get near 0F. That might be ideal for a keezer temp sensor, beause you'll operate near there. But better is to get a pitcher/bucket of water and let it sit at room temperature. Give it like a day to stabilize. Then you'll be around 65-70F, which is right around prime fermentation temperature. You want it stable so you're not trying to align to a moving target, or dealing with some weird hot/cold spot. Pick one temperature sensor to be your "gold standard". Then do the "calibration" on all of your equipment in that same bucket of water. I did all of my Tilts, my Inkbird controllers, plus multiple other controllers all at one time, using a Thermowerks thermometer as my standard. This can help reduce potential error between your controller (which you're using to adjust your temperature) and your Tilt (which you're using to decide if your controller is doing a good job).
3. Temperature stratification is real. Top is warmer than bottom, especially if you're in the process of heating or cooling. Your beer is circulating naturally to this order of things. If your Inkbird is at the midpoint height of your bucket and your Tilt is floating up top, they're going to be different. Point #1 of insulation wrap helps reduce this effect. You'll also have stratification from outer ring of our bucket to the middle/center of your bucket. This will get better after you get your beer at your target temperature, as long as you're patient and you're using the insulation mentioned above.
Below is a screenshot from my Tilt running in a fermentor right now. I had to warm it up a bit at start, so you can see some oscillation at start. The controller of course things it's holding things within a degree, but the stratification of layers inside at different temperatures takes some shuffling around until everything gets evened out. In this case, I'm using a temperature probe in from the side wall of my conical, about at the mid-height of the beer. The conical has a neoprene jacket on it. Tilt floating up top, and heat wrap down at bottom at transition from straight to cone section.
