I know JoshP said Delta-Force's answer is a copy of Shannon's answer, but let's make this super clear in one spot.
As Delta-Force says, you may to need to set this in two places, the one the OP mentioned (AutoFormat) AND the one Shannon mentioned (AutoFormat As You Type).
I found a place that describes this reasonably well for Word, and I'll edit those instructions to describe Outlook here:
- On the File tab, click Options.
- Click
Mail, then Editor Options and then click the AutoCorrect Options button.
- In the AutoCorrect dialog box, do the following:
- Click the
AutoFormat As You Type tab, and under Replace as you type, select or clear the "Straight quotes" with “smart quotes” check
box.
- Click the
AutoFormat tab, and under Replace, select or clear the "Straight quotes" with “smart quotes” check box.
- Click OK in the AutoCorrect dialog.
- Click OK in the Editor Options dialog as well.
- Profit.
Here they are in all of their duplicitous glory.

Do both.