I have a few comments/questions, in no particular order…
You haven’t found William arriving c1850s. Are the Australian passenger records fairly complete? Is it unusual to
not find someone? Different countries involved, but I’ve found very few passenger records for my ancestors who sailed to North America c1850s. I believe not finding a passenger list is the norm for Canada/North America during that time frame.
Missouri, Kentucky and Tennessee have been mentioned. While my own ancestors settled in Ontario, Canada, they remained in the same general area for generations. However, hubby’s paternal side moved from state to state pre-1890, living in Tennessee, Alabama, Georgia and Arkansas so I’m not surprised to find Stover, Fisher and Jones meandering as well. (The same is true for a few other searches I’ve done.)
Catharine was about 30 years old when she married Francis Jones. A bit old to be marrying for the first time but not uncommon I suppose. Perhaps if she did have four children prior to her first marriage, there is a logical reason (such as no local church, cost to get married, etc.).
William F/William T on the 1850 census. To me, the initial closely resembles other F’s on the page. The T’s on the page are a bit different, I think. If it was an F, perhaps his actual name was William Frederick Tinsley, William Francis Tinsley, etc.
If I’m remembering correctly, the four children born prior to the 1839 marriage were not included with their mother in the 1860 census. Possibly due to their ages, did they refuse to move to Texas with their mother, did some die, etc. I wonder if they could be found in 1860 additional clues might be uncovered. (Perhaps details have been found, I didn’t reread all of the comments and I don’t think I found anything.)

Neale1961 raised a good point about William sailing under a different surname.
Regarding the 1860 census, perhaps Jones was the name that Francis or Catharine gave the enumerator. But, that doesn’t mean that they actually legally changed their names. It could have been a mistake by the enumerator or the parent intentionally misled the enumerator. Or, perhaps all of the children were known as Jones in the town.
Trying to find out more about William Tinsley, born c1809, Kentucky might shed additional leads. (I briefly looked around but didn’t find anything.)
I also have not run across the name Narcissa before, but most of my research has been in Canada and the UK.
I agree with Neale1961; even official documents can contain errors.
Something to keep in mind, depending upon how strict laws were then, there could be a slight chance that Catharine had been married to a Tinsley and chose not to share that name on the 1839 marriage certificate.
Apologies for the lengthy comments.
