Steps to Reproduce:
Host a server then join it
Use an repeating command block that always executes /title @p actionbar "Hi!"(I recommend this one the most.)
Get further away from the command block or travel to another dimension.
Observed results:
The command block doesn't say "Hi!", however your chunks can't see him.
Expected results:
The command block should work as it does on singleplayer.
The behavior on singleplayer is no different than on servers/multiplayer. When you were testing in singleplayer, you most likely placed the command block within the spawn chunks.