Diagnosing a chattering AC fan relay
it's chattering because the thermostat loop already has a relay in series with the supply so there is not a full 24V when you interrupt that circuit.

Undervoltage makes relays misbehave.







simulate this circuit &ndash; Schematic created using CircuitLab

the parallel connection you have used is one solution, another could be to connect the fan relay in parallel with the solenoid output, but then the fan would only run when the heat was active.