My device is running iOS 27 and I have three AirTags two of which are with me and one shared. All of them are displaying the correct location and do not move as described in your post by you.

When an AirTag appears to be moving from one place to another even though it is actually with you, the first thing to check is whether you are looking at the correct AirTag in the Find My app. If you have multiple AirTags associated with your Apple Account, it is easy to select the wrong one and mistakenly interpret its location as that of the AirTag you are carrying.
It is also important to understand how the Find My network works. If your AirTag is with you and remains within Bluetooth range of your iPhone, your iPhone can communicate directly with it. In this situation, the AirTag's location is determined through your own iPhone, and the presence of other people's iPhones nearby does not cause their devices to report their locations to you.
For example, suppose several people carrying iPhones walk past you while your AirTag is in your bag. Their iPhones do not simply send their own locations to your Find My app because they detected your AirTag. The Find My network is designed to detect the AirTag and securely relay the AirTag's location, not the location of the person or iPhone that happened to detect it.
The situation changes when the AirTag is outside the Bluetooth range of your iPhone. Your iPhone can no longer communicate with it directly. If the AirTag is subsequently detected by another Apple device participating in the Find My network, that device can securely and anonymously relay the AirTag's approximate location to Apple's Find My network. Your Find My app can then display the AirTag's updated location.
So, in simple terms:
- AirTag within Bluetooth range of your iPhone: your iPhone can communicate directly with the AirTag and update its location.
- AirTag outside your iPhone's Bluetooth range: your iPhone cannot directly locate it.
- Another compatible Apple device detects the AirTag: that device can anonymously report the AirTag's locationto the Find My network.
- Other people's iPhones passing near an AirTag that is with you: they do not report their own locations to you.
Therefore, if an AirTag that is physically with you appears to be jumping between different locations, verify that you have selected the correct AirTag first. If the location history continues to show distant or apparently unrelated locations while the AirTag is definitely in your possession, the issue may instead involve delayed location updates, the Find My network, or another AirTag being selected.
One important distinction is that Find My does not use other people's iPhone locations as a substitute for your AirTag's location. It uses other Apple devices as anonymous relay points to determine and report where the AirTag itself was detected.