All I know I have never had my 15 ED or current truck, 19 5th Gen "relock" themselves after remote starting the vehicle and hit unlock. Of course, when U remote start, the vehicle cycles through various parameters, like insuring all doors secured-truck locks them, hood down, no MIL present, before remote system will even work. All I can relate is what my 5th Gen does and what my ED did, had a II Gen ED before this 5th Gen.
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In U connect Settings, there are various options and conditions you can set ref remote start. Way too many pages to copy/paste here.
OP suggest you look in yer manual and/or download manual so you can review. Of course depends upon year of truck and sometimes Trim Levels on what options are available.