You are exactly correct. My ancestor, John Hermy Robinson of Austin, Travis County, TX was considered to be a unionist and did indeed sign the anti secession petitions in Travis County. He wrote the following letter to the local newspaper that explained his sentiments.

On 27 Apr 1861 the State Gazette published the following letter by John H. Robinson written to the paper’s editor, Major John Marshall:

Austin April 18, 1861
Sir – Knowing a wrong impression is abroad in our State, as regards the feelings of the citizens of Travis county, and believing you would render your aid to remove same, I have troubled you with my own observations, obtained through a business intercourse with many of our people. Many, very many, citizens of our city and county believed Southern rights could be secured by a cooperation with the slave holding States, and, so believing, voted against secession, I among the number. Yet, I hold myself second to none in Southern patriotism. As soon as the people had spoken, we, as good Democrats, believing the people should rule, rendered a willing acquiescence to their verdict, and hold ourselves ready, with might and means, to help the Southern Confederacy.

I hold an office in the city in which there is neither profit or praise. [Robinson was an alderman] Yet, though called a Union man, I promptly repaired to the Mayor’s office to register my oath, the laws of Texas and Constitution of the Southern Confederacy to support. Hundreds are like unto me, who voted as I did, with an earnest conviction that the remedy was inside separate secession. True, there are men among us with northern sentiments, presuming upon our vote. Who dare to class us as aiders and abettors of Abe Lincoln and his Black Republican crowd? Let their most prominent leader come among the citizens of Travis county, and try to enlist from the so-called Union men a corporal’s guard to oppose secession and they would fail, wretchedly fail.

J. H. Robinson, merchant