Correct tense of venir in example

SR, 

you are right - it is the subjunctive.

 ' Avant que ' takes the subjunctive mood, and ' venions ' is the subjunctive mood in present tense in the relevant examples.  The 'ne explétif' has also been included, although would mostly be dropped in speech nowadays.

(This is not to be confused with the imparfait form, which has the same spelling. For most verbs other than some of the 'irregular' verbs,  the nous and vous subjunctive forms have identical spelling to the imparfait form, so context informs which it is)

Avant que + ne explétif + the subjunctive mood (Le Subjonctif) = Before I do in French

https://www.wordreference.com/conj/frverbs.aspx?v=venir