Minecraft 1.20.5 has changed syntax on many commands, so most commands will no longer work without an update.
An update is in progress, you can check compatibility progress here.
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Try the Commands Troubleshooting and Help page if you get stuff with server errors.
Minecraft Illusioner NBT Data Tags
Using the summon command to spawn in a minecraft illusioner is simple, take the command and enter into chat and presto you have an illusioner. Illusioners are Java edition only.
How to set the Illusioner's spell cooldown
Illusioners cast a number of spells, this spell casting ability has a cool down timer known as SpellTicks. When set to a positive value it will tick down (20 ticks per second). When reaching zero the Illusioner can cast a spell.
/summon minecraft:illusioner ~ ~ ~ {SpellTicks:200}Suggestions or found a bug
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If you're looking for a particular summon mob generator you can link to these specific versions of the command generator.