This is pronounced incorrectly. "matin" should sound like "mah-tahn", not "may-tahn"
I have just listened to it and it sounds right.
That might be a regional pronunciation difference. There are some big vowel differences between, for example, "Quebec" french and "France" french (an oversimplification of both regions...).
The pronunciation is "average French from France".
Would this also mean 'this morning'?
Actually, "this morning" means "ce matin" but "that morning" would be better translated by "ce matin-là" (another morning in the past or in the future)