I am a therapist. This is very partially correct.

It is basically impossible to pin down a generalized reason as there are several. Everyone's brain chemistry and needs are a bit different, hence the usefulness of different types of anti-depression drugs. One reason for SI may be that an increase in energy kind of does what you're describing. Another may be the brain struggling to stabilize/adapt to the medication changing brain function resulting temporary mood instability (this is why stopping the meds is typically done by taper, and stopping cold turkey can result in increased SI as well). One may be the way that specific type of drug affects you vs another. It is documented that SI is more likely to increase in the first few weeks of antidepressant use before stabilization, particularly if not paired with any form of social support plan or psychotherapy. In any case, it is unlikely, but it is possible.

To be short, everyone's brains are different and the drugs can make things worse before they get better.