Just in case you don't know, the circles you see centered on other fleets are their sensor radius. This radius will go down when your own sensor profile is smaller. If you are inside these circles when you turn your transponder off, they will chase you for turning it off. If you get inside these circles with your transponder off, they will chase you. If you turn your transponder 'on' and you suddenly appear in their scanners, they will chase you (because you were obvious just previously running dark).
Maybe the sensor profile of your fleet is just too high. Some things you can do: Install militarized subsystems on your civilian craft to halve their sensor profile (it also boosts their burn by 1, making it absolutely essential for most of the game). Install insulated engine assembly on your ships to halve their sensor profile. Leave ships with "loud" D mods in storage for the delivery.
You can also do things like go far away from the planet with your transponder off, then do a sensor burst: you will show up on their sensors and they will leave to chase you, drawing them away from the station. Go sideways, then dodge around them and go in.
However, if the patrols you are trying to dodge are both faster than you and you have a bad sensor profile... good luck!