Debió haber vs. debe haber

Debió haber vs. debe haber
 

Do these sentences mean exactly the same thing?
He must have had the interview yesterday.

Él debió haber tenido la entrevista ayer.
Él debe haber tenido la entrevista ayer.

Yes, although debió is in past tense.

I was surprised to see that must can be used in past tense, instead of to have.

But then again, I do not my own grammar, much less English grammar. :-)

Here's the difference in my mind (disclaimer: Spanish is not my first language).

There are two uses for "debió haber ____past participle____".

1. Supposition. (debió haber OR debe haber)

-- ¿Donde está Javier?
-- Debió haber ido a la tienda. :good: Debe haber ido a la tienda. :good: (He must have gone ...)

2. Saying what someone should have done. (only debió haber [not debe haber])

Natalia iba a hacer un pan y tenía poca harina, pero pensó que le iba a alcanzar. Resulta que no alcanzó la harina.

Natalia debió haber ido a la tienda para comprar más harina.
Natalia should have gone to the store to buy more flour.

For this one, you could also use hubiera.

Natalia hubiera ido a la tienda para comprar ....

Exactly. In my mind you have to use "should" or "had" accordingly. I did not know "must" could be conjugated in past tense.