In general, Relevanssi doesn’t store any information about users and doesn’t share any information outside your own server. There are, however, two exceptions.
If you enable logging, Relevanssi will log all search queries, except from those users you block in the settings. The logs will always include the user ID and if you so desire, the user IP address. It’s not currently possible to disable the logging of user IDs, but this will be included in the next version of Relevanssi (Premium 2.1.6, free 4.0.10).
Versions 2.1.6 and 4.0.10 will include tools to remove data from the logs. If you use the WordPress privacy tools to remove user’s data completely from the system, that will automatically remove all log entries with their user ID. Relevanssi can’t automatically remove log entries for searches users do when they are not logged in, as Relevanssi cannot connect IP address to user ID, but there will be a tool to remove log entries based on IP address.
Indexing attachments with personal information would mean that the personal information is being shared with third parties. This is why it is forbidden to use Relevanssi attachment indexing to index files that contain personal information. We do not know what is in the files you index on our servers and thus can’t stop you from doing it, but it is still forbidden to do so.