Based on what you have written, you need to be honest when answering any employment questions. If you fail to answer honestly, then upon discovery by your employer your employment may be terminated for lying on your application. There are a few options available to you with fixing any un-wanted disclosure of your criminal records. You should consult with a local law firm to fully discuss your options regarding your criminal record.
The above response given is not intended to create, nor does it create an on-going duty to respond to questions. Additionally, the response does not form an attorney-client relationship, nor is it intended to be anything other than an educated opinion. It should not be relied upon as legal advice. The response given is based upon the limited facts provided by the person asking the question. To the extent additional or different facts exist, the response might possibly change.
"Disposed" just means that a case was taken care of and is no longer pending on the court's docket.
What actually happened with your case? Were you convicted? Was the case dismissed? Did you plead guilty? Did you get probation? Deferred Adjudication?
As far as answering the questions for employment, if the question asks you if you have ever been arrested, the answer would be yes, unless you have had an expunction. If the question asks if you have been convicted, that depends on the outcome of your case. Deferred Adjudication is not a conviction unless a Motion to Adjudicate has been granted.
So it really just depends on what the employment question is asking and what actually happened with your case. Assume an employer will see everything unless an Expunction or a Petition for Non-disclosure has been filed.
If by "completed the deferred," you mean you successfully completed the deferred probation and were subsequently discharged from probation you would have to admit "yes," you have been previously arrested and/or placed on deferred community supervision. UNLESS, you were able to have that deferred expunged. If it's expunged, you can pretend like it never happened. If it's just a completed deferred, you can say you've never been convicted of that particular crime. The arrest is still there though. Hope that helps. Good luck.