My compressor has a 240V magnetic starter (big relay) and a 120V activation coil (small solenoid). I have a light switch that enables the pressure switch that turns on the coil when pressure is low. I could add a timer in place of the switch or add a timer as well as the switch.
The mag-starter or contactor contacts just switch on the pump motor--they're straight through.
The coil, pressure switch, switch and possible timer are all wired in series (one after the other) with the hot at one end and the neutral at the other. The hot obviously feeds from the switch side, and the end of the coil is tied to neutral.
Think of it in steps. Start with the contactor coil wired directly to 120V--it runs all the time. Add a pressure switch from the hot side. Next add the timer (just another switch). If desired add the master shutoff switch.
Hot---master switch---timer---pressure switch---contactor coil---neutral
The above is pretty much the same as the OP described.
BTW, you can get a little neon test light in the electrical section at the HW store for a few bucks that will show the hot by touching one end to your skin and the other to a wire. It will glow dimly. Across a hot and neutral (120V) it glows brightly, and across 240V glows very brightly. Example:
https://www.tequipment.net/Triplett/...RoCctkQAvD_BwE