What could cause a central A/C system to smell but only after central heating had been used?
Smells in AC systems are somewhat common.
When the heat is used the drip pans dry out and any gunkies (a professional term for growth in the drip pan).
When the AC is used the dormant gunkies get some moisture and come to life.
The moisture is normal when the AC is on.
Ways to reduce or eliminate this growth add condensate pan tablets or strips that kill the gunkies without stinking the house up, bleach will work diluted but it stinks.
My normal mold treatment is a no no (hydrogen peroxide) DO NOT use any acids as they will eat the galvanized treatment off the drip tray and etch the aluminum parts.
You really only need to use these during cooling seasons not during heating because when heating there is no moisture in the pan. The tablets, strips or whatever use the moisture to kill the active fungus in the gunkies.
The gunkies are dust with mold / fungus growing and they can build up and block the condensate drains,  produce bad odors and create health hazards like legionnaires (first found in commercial AC systems). Simple sanitizing tablets or strips prevent the growth and can be purchased at most home stores.