You must pass Nex's test but you can travel to a different time. Don't get too comfortable. Nex will be much stronger this time around.

When you defeat Nex, the Time Gate to the year 2099 will open.

You won't be authorized to travel time unless you defeat Nex the Gatekeeper of Time.

Ah, you've passed Nex's second test. Now then, you should be able to access the Time Gate to the year 2099.

Take the Time Traveler's Pocket Watch and go through the Time Gate.

Come back after you've passed Nex's test. Nex the Gatekeeper of Time lives inside the Old Tree of Tera.