Texas trespassing law requires you to be legally trespassed first (asked to leave by the cops) then if you refuse to go you can be arrested.

IANAL, but AFAIK that is not strictly correct. The actual code is:

Sec. 30.05. CRIMINAL TRESPASS. (a) A person commits an offense if the person enters or remains on or in property of another, including residential land, agricultural land, a recreational vehicle park, a building, or an aircraft or other vehicle, without effective consent and the person:
(1) had notice that the entry was forbidden; or
(2) received notice to depart but failed to do so.
(b) For purposes of this section:
(1) "Entry" means the intrusion of the entire body.
(2) "Notice" means:
(A) oral or written communication by the owner or someone with apparent authority to act for the owner;
(B) fencing or other enclosure obviously designed to exclude intruders or to contain livestock;
(C) a sign or signs posted on the property or at the entrance to the building, reasonably likely to come to the attention of intruders, indicating that entry is forbidden;

So you need to be notified either verbally or by posted notification (or something obvious like a fence). The only time you are given an opportunity to depart is if you receive notice after the fact (like verbally). If you ignore a posted sign, they can arrest you then and there without any further notice or opportunity to depart (though in practice they usually will).