Help! Power question

A 5 ton unit can have over 100 amp inrush current on startup. Start kit ( capacitor and potential relay) will smooth that out. 

Did you go back with same btu on air conditioning unit?

Agree with acman3 and ghosthouse. The service factor on startup may be causing a temporary drop in voltage. Logic circuits usually use a 5VDC supply. You may be able to get as low as 4.5VDC and still be safe. 115VAC through a step down transformer to yield 4.5VAC is a 25x reduction in voltage. If the line voltage dips to 100VAC, the voltage on the secondary side will drop to 4VAC. Rectification has little to no affect on voltage. At 4VDC the logic circuit would likely freeze and not function until a complete reset of the logic circuit is performed. 

220VAC supplied circuits will use both legs of the service being supplied. Startup will affect all service since the 220 breaker uses both supplied phases. You said when the air kicks on. Not sure where you are located but here in TN we haven’t used the air in months. Is this a heat pump in heat mode?  

You may be able to prove this by testing using a uninterruptible power supply/battery backup unit like used on computers.   This should keep the line voltage stable. 

Just a thought. 

The start of the condenser is causing a whole house voltage drop. I’ve seen this and I’m wondering if the wires leading to the condenser are undersized. You only need a 200 amp service panel if you have a larger home( over 3500sq/ft). 
A/c units normally draw about 25amps during start up that’s why you have a 30 amp breaker connected to it. I would have an electrician check out the work that was done. He/she will find out what’s going on very quickly. 
Giid luck!

Surge protectors do not guard against voltage sags, they absorb the punch of a voltage spike.

Do the lights dim? Not just a tiny bit, but a lot. If that is the case, then have the electrician to check -- in addition to the HVAC contractor's work -- the wiring to your dedicated outlet and the rest of the house. If you have aluminum wires from the meter to the main panel lugs, have him check those. It's not uncommon for the lugs to loosen over time causing oxidation at the contacts and making voltage sags more serious than they have to be.

AC units draw a lot of current on startup and it's not uncommon (or abnormal) for the lights to dim a tiny bit. The power supply of your pc and dac easily compensate under this condition. But if the voltage drops too low, it confuses the voltage regulators in your electronics and things can stop working.