You can automate parameters in iZotope Vinyl using host applications that support effects automation. Automation allows you to specify changes to parameters over the duration of a mix.
The implementation and specifics of automation are dependent on the host application, so we refer you to the documentation of the host app for setting up an automated mix. In general, though, you patch iZotope Vinyl as an ordinary effect on a track, then in the track view of the host app assign automation envelopes to it. These envelopes control how iZotope Vinyl parameters are changed over the course of the mix. In this case, most of your "tweaking" is done in the track view of the host app, dragging curves and envelopes as opposed to changing controls in iZotope Vinyl.