Were parts of the Universe deflating during Inflation?
That sounds... confused, or else just wrong. Negative pressure is what causes inflation: something (inflaton field, cosmological constant, or "dark energy" in general) with an energy density that stays approximately constant as space expands has negative pressure and will drive the exponential expansion of space.

The transition to "true" vacuum is what shuts off inflation, after which you get  the standard Big Bang, during which the expansion continues but slows down.

(The cosmological constant -- or "dark energy" -- also has negative pressure, and so the universe is gradually moving towards a state where the space between galaxy groups and galaxy clusters will again be expanding exponentially.)

The "eternal inflation" model has our visible universe -- almost certainly a tiny part of a much larger region of true vacuum -- as one of many such pockets of true vacuum embedded within a vastly larger false vacuum that's still expanding exponentially.