Spawn zombies every tick

The 'wait 20 ticks then on server-side' block does not act like a timer, it acts as a delay, which are different. To explain what is happening, the procedure is triggering every tick, and when it gets to the delay, the current iteration of the procedure pauses, but new iterations are still able to start. This leads to what you are saying, where it waits one second, then spawns every tick.

The solution to fix this would be to set up a potion effect, variable, or nbt-based timer. An example is where an nbt number value is increased by 1 on the player, every tick the condition is active, then, when it reaches 20, you summon a zombie and reset the nbt number to 0.