I'm afraid this is becoming a habit on Dragonball Super questions, but the current answer as of Episode 98 is that we do not know.
The Saiyans from Universe 6 don't seem to have names for their forms. One could guess that is because they're currently only Super Saiyans - just as we didn't have the name Super Saiyan 2, or Ascended Saiyan until our Universe 7 Saiyans reached those forms.
Outside of the Universe 6 Saiyans saying "I feel I've reached a level above Super Saiyan"/"I feel I can change form again!" or a Universe 7 character saying "I can't believe you've already reached Super Saiyan 2!" we won't know for sure.
I would say we'll need to stop using Aura's as proof of forms. Not only do we not know if the Universe 6 Saiyan transformation is completely analogous to Universe 7 (since Universe 7 Saiyans never transformed by focusing on a single spot on their back), we also have seen Goku and Vegeta create a Ki-Aura to stop Lavender's poison attack yet was thought in at least one question on this site to be some new form. Plus, IRL we have the animators using new animation styles - they may just like using lightning around Caulifla to visually represent how she is a "cut above" the average Super Saiyan even in base form.
Edit: as of episode 100, we have Caulifla specifically say she went Super Saiyan 2 in the same day however she did say that she was unable to return to that form until Goku went Super Saiyan 2 to show her, so I'd say she didn't "learn" Super Saiyan 2 on that day. This is backed up by her going into what a Dragonball Wiki calls Super Saiyan Third Grade (The big-muscle "power but no speed" SSJ form) instead of going SSJ2 - just like when Goku and Trunks did when they hadn't reached SSJ2.