Like almost all questions, there is no one black and white answer. For one, the Imperiums view on psionics differs depending on the time period.
The Psionics Suppressions ran from 800 to 826 and resulted in the closure of almost all psionic research and teaching establishments as well as the criminalisation of psionic power use. Prior to this, psionic training and use was not illegal in the Imperium. My guess is that prior to The Psionics Suppressions the Imperium would not have interfered with however the individual worlds wanted to handle it, from burning at the stake to actively researching psionics or even allowing religions that worshiped them.
Another item that adds variety to an answer is who caught the psion?
"The Imperium continues to conduct psionics research in order to counter the use of psionic powers by foreign agents (such as the Zhodani) or illegal users." - so one option might be that captured psions become test subjects in secret Imperial research institutes.
Mongoose Book 5 Agent has a section that covers the different law levels worlds might have. One part addresses psionics with descriptions of how psionics is treated depending on a worlds law level. To me, this implies that worlds are allowed to handle this without needing to notify some Imperial Psionic law enforcement. The descriptions range from
"The government has a strict ‘no tolerance’ policy for anything at all related to psionic ability, technology or genetics. Psions are sterilised, lobotomised or worse."
to
"With only the basest regulations on psionic abilities, the government feels it necessary to keep track of convicted psi-offenders or psions with particularly dangerous talents. The government does not restrict these abilities but needs to know who has access to them."
Other options include registering all psions, chemically or surgically suppressing psions, deportation, worlds may restrict the use of selected psionic abilities while others are allowed, all psions are required to work for the government and so on.
I don't have time to look through the different racial material to see how the Imperium treats psionic travelers from outside the Imperium, like Droyne.
