why, when I heat liquid in a sauce pan on my stove is there an
immediate increase in steam when I turn off the heat?

Answer depends on exact meaning of the word 'steam'

http://www.answers.com/steam&r=67

When you switch of the 'influx of heat' temperature starts decreasing, so

For meaning 1.a (above) answer is certainly : NO.

For meaning 1.b (above) = visibile mist = droplets of water re-condensed 
from water vapour, answer  could be : YES in a very cold room or outside.

Here is one guess:  you can't see steam, but you can see liquid water
droplets.  As steam cools, it condenses into droplets.  The air above
the pot quickly cools when you turn off the flame, causing a momentary
increase in the rate of condensation.

In addition to rracecarr-ga's comment, I wonder if hot air rising from
the burner acts like an air curtain to keep colder air away from the
area immediately above the pan? Once the heat's removed, cold air can
get in and there's more condensation.

Ian G.