> Where is Markrae when you need him?
You called...?
It's simple enough.
On the contrary implies a deliberate contradiction of the previous statement. E.g.
"That must have taken you hours!"
"On the contrary, it took no time at all."
In the above dialogue, you would not say "To the contrary, it took no time at all."
To the contrary, however, is used when you are demonstrating (or asking for) proof that something is the opposite of what has previously been claimed. E.g.
"The Americans definitely went to the moon!"
"I can show you plenty of evidence to the contrary."
In the above dialogue, you would not say "I can show you plenty of evidence on the contrary."