Serious adverse events from spinal adjustment are rare. The most common effect by a wide margin is mild soreness for a day or so after a visit, in the same way you might be sore after starting a new form of exercise.
Where safety actually comes from
Mostly from case selection rather than from technique. That means examining properly, recognising the presentations where manual treatment is not appropriate, screening for the conditions that need a doctor instead, and referring rather than treating when that is the right call.
It is the reason a first visit here takes 45 minutes. A thorough examination is not only how you work out what to do: it is how you work out what not to do.
You have a say in the technique
There is more than one way to restore movement to a joint. Some presentations suit a manual adjustment; others suit a low-force approach using an instrument or a drop-piece table. If you would rather not have a particular technique used, say so: there is almost always another way, and being tense about what is coming is counterproductive anyway.
You will be told what is about to happen before it happens.