Yes, that is what an extradition treaty is.
If it didn't, the treaty would say you have to prove guilt in court before being extradited.
Well that’s just not accurate. From the 1979 treaty:
OBLIGATION TO EXTRADITE
(b) For the offense of association to commit a crime under the laws of Turkey and for conspiracy under the laws of the United States when the facts establish an offense under the laws of both Contracting Parties;
So yes, when trying a conspiracy case, evidence is required before extradition can be granted. You can’t just request the other country send back your nationals for a conspiracy trial without evidence that a crime was committed. That offense of association would also have to meet the requirements for an offense under US law as well. Furthermore:
CONDITIONS OF REFUSAL
(1) Extradition shall not be granted:
(a) If the offense for which extradition is requested is regarded by the Requested Party to be of a political character or an offense connected with such an offense; or if the Requested Party concludes that the request for extradition has, in fact, been made to prosecute or punish the person sought for an offense of a political character or on account of his political opinions.
So the Requested Party (the US) can refuse extradition if it is believed that the extradited party is only being punished for their political opinions. This would require Turkey to provide some evidence that there was an actual criminal offense committed, and that his prosecution would be related solely to that offense, not just because he’s a critic of Erdogen. Finally:
CONTENTS OF THE REQUEST
(1) A request relating to a person being prosecuted or who is charged with an offense, and who has yet to be convicted, shall be accompanied by the following:
(a) A warrant of arrest issued by a judge or other competent judicial officer;
(b) A statement of the facts of the case;
(c) Such evidence as, according to the laws of the Requested Party, would justify arrest and committal
for trial of the person sought if the offense had been committed in the territory of the Requested Party;
(d) [*10] Evidence proving that the person sought is the person to whom the warrant of arrest refers, including information, if available, on nationality; and
(e) The text of the applicable laws of the Requesting Party, including the law defining the offense, the law prescribing the punishment for the offense, and the law relating to the limitation of legal proceedings or the enforcement of the penalty for the offense.
So in order to request extradition, yes, evidence has to be provided, sufficient to justify a warrant under US law. If this standard is not met, than the US has no obligation to extradite anyone to Turkey.
The full text of the extradition treaty:
https://photos.state.gov/libraries/turkey/461177/pdf/32t3111.pdf