The rules for Wild Magic Surge are:
Immediately after you cast a sorcerer spell of 1st level or higher, the DM can have you roll a d20. If you roll a 1, roll on the Wild Magic Surge table to create a random magical effect.
And the rules for Tides of Chaos are:
Starting at 1st level, you can manipulate the forces of chance and chaos to gain advantage on one attack roll, ability check, or saving throw. Once you do so you must finish a long rest before you use this feature again.
Any time before you regain the use of this feature, the DM can have you roll on the Wild Magic Surge table immediately after you cast a sorcerer spell of 1st level or higher. You then regain the use of this feature.
How do these features interact with each other? I see two options:
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They are the same roll. If the player has used their Tides of Chaos, any roll on the surge table will reset it.
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They are different rolls. So only a roll specified as resetting Tides of Chaos would do so, and any other surge would not. By extension of this the DM could have the player get 2 surges on one spell, 1 for Wild Magic Surge and 1 to reset Tides of Chaos.
Our play group is not sure which is the correct option to use.
Best Answer
There is nothing to prevent you from being made to roll twice on the table.
They are two separate class features, if you've used Tides of Chaos, the DM is well within his rights to make you roll the d20 to check to see if you need to roll (for casting a spell), and making you roll on the table to get Tides of Chaos back.
That's not to say he should, however there might be a few situations where he would. The way I envision this working is that he asks for a d20 roll to check to see if you go to the table, and you pass it. Then he might also mandate that you roll on the table to get back your used Tides of Chaos advantage.
These class features appear to be mutually exclusive and as such are invokable together on any spell cast. Your second interpretation is correct.