When a student has chosen to continue their education, they have also started towards being financially secure in life.

has chosen is part tense participle

Is "have also started" present perfect tense?

"has chosen" is the verb in the dependent clause; it's present perfect.

"have also started" is the verb in the main clause; it's present perfect.

Do you see the error in pronoun/antecedent in this sentence, though? It's pretty glaring.

http://grammar.ccc.commnet.edu/grammar/pronouns.htm

See #2.

When a student has chosen to continue their education, they have started towards being financially secure in life.

Is that better?

or this...

When a student has chosen to continue his or her education, her or she has started towards being financially secure in life.

You could keep your second correction. It'd be better, though, just to use plurals.

When students have chosen to continue their education, they have started being financially secure in life.

Thank you very much!!! The verb tenses are both present perfect?

Yes, they are.

And you're very welcome!