They say I need a treatment too.

This is a tricky one, and this answer is only for subterranean termites (not for drywoods and not for dampwoods).

Let’s say the termites are in your neighbor’s house. A nearby infestation means that local conditions are suitable for the termites and so it tells you that your place is also at some risk. If baits or another colony-killing method is used, then that immediate risk to your house is gone as that colony will be controlled. But there may well be many nearby colonies. If they just repair the damage or poison the ground with a repellent chemical (like bifenthrin), then the termites may be ‘pushed’ towards feeding at your place. That isn’t good.

On the other hand, the termites may be living in your house and have spread to your neighbor’s. Or they may be nesting in your yard.

In any case, this is not the time to sign up for a treatment. You should get a proper timber pest inspection done so that you can assess your options. Then talk to your neighbor about the best way to do things.