You might need to explain what the "multi project picker" field is, as it's not part of the core.
If it is the plugin I'm thinking of, then the answer is "nothing". The picker is just a way of listing several projects against one issue. It has no effect on the workflow because the issue you are looking at is still in one project and hence uses that project's settings. (Although you could start doing stuff in the workflow that looks at the field)
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