In American spoken English, in the last twenty years or so, the word totally is used in a way that was not used before:
It is basically slang or looser speech.
Example: "I totally don't understand". Meaning: I really don't understand.
In formal conversation between high-level speakers you probably would not hear the sentence above.
All the examples given by the OP reflect this usage. The Huffington Post one is probably spoken English, too.
Generally, in the past, totally, completely and absolutely were used in declarative sentences or negatives ones like this:
I completely or absolutely understand.
I understand completely or absolutely [less common but used]
I don't completely understand. [absolutely would not be used here].
In the past, totally was only used in declarative sentences:
"I totally understand".
This usage of totally is similar to the usage of so.
"He so isn't into it." for: "He isn't into it at all".
[idiom: to be into something; to like it]