In terms of DCS mechanics, what is actually happening here is that the AI MiG-19 detects your radar emissions on RWR. I quickly tested it and an AI MiG-19 will detect and engage a F-15E at a distance of 210 km. Considering the quality of the MiG's radar warning receiver this is obviously completely ludicrous.
When the F-15E is not emitting on radar it is actually possible to test the AI MiG-19's own radar performance. It will then detect and engage the Strike Eagle at 50 km distance in either look-up or look-down situation. This is still waaay over the top. According to the RAZBAM manual it has a maximum search range of 12 km. Also it should not be look-down capable at all.