Look's like you want "d-MMM" as your format instead of "dd-MM". See the following page for reference.
t = readtable("TNdatafix.csv",VariableNamingRule="preserve",TextType="string")
t = 320×7 table
STATION DATE DLY-PRCP-25PCTL DLY-TAVG-NORMAL DLY-TAVG-STDDEV MTD-PRCP-NORMAL YTD-PRCP-NORMAL
_____________ ________ _______________ _______________ _______________ _______________ _______________
"USW00013893" "1-Jan" 0.05 42.7 10.6 0.16 0.16
"USW00013893" "2-Jan" 0.05 42.6 10.6 0.32 0.32
"USW00013893" "3-Jan" 0.05 42.5 10.7 0.48 0.48
"USW00013893" "4-Jan" 0.05 42.4 10.7 0.63 0.63
"USW00013893" "5-Jan" 0.05 42.3 10.7 0.79 0.79
"USW00013893" "6-Jan" 0.05 42.2 10.7 0.93 0.93
"USW00013893" "7-Jan" 0.05 42.1 10.7 1.08 1.08
"USW00013893" "8-Jan" 0.05 42 10.7 1.22 1.22
"USW00013893" "9-Jan" 0.05 42 10.7 1.36 1.36
"USW00013893" "10-Jan" 0.05 41.9 10.7 1.5 1.5
"USW00013893" "11-Jan" 0.05 41.8 10.7 1.64 1.64
"USW00013893" "12-Jan" 0.05 41.8 10.7 1.77 1.77
"USW00013893" "13-Jan" 0.05 41.7 10.7 1.9 1.9
"USW00013893" "14-Jan" 0.05 41.7 10.7 2.03 2.03
"USW00013893" "15-Jan" 0.05 41.7 10.6 2.15 2.15
"USW00013893" "16-Jan" 0.04 41.6 10.6 2.27 2.27
t.DATE = datetime(t.DATE,InputFormat="d-MMM")
t = 320×7 table
STATION DATE DLY-PRCP-25PCTL DLY-TAVG-NORMAL DLY-TAVG-STDDEV MTD-PRCP-NORMAL YTD-PRCP-NORMAL
_____________ ___________ _______________ _______________ _______________ _______________ _______________
"USW00013893" 01-Jan-2022 0.05 42.7 10.6 0.16 0.16
"USW00013893" 02-Jan-2022 0.05 42.6 10.6 0.32 0.32
"USW00013893" 03-Jan-2022 0.05 42.5 10.7 0.48 0.48
"USW00013893" 04-Jan-2022 0.05 42.4 10.7 0.63 0.63
"USW00013893" 05-Jan-2022 0.05 42.3 10.7 0.79 0.79
"USW00013893" 06-Jan-2022 0.05 42.2 10.7 0.93 0.93
"USW00013893" 07-Jan-2022 0.05 42.1 10.7 1.08 1.08
"USW00013893" 08-Jan-2022 0.05 42 10.7 1.22 1.22
"USW00013893" 09-Jan-2022 0.05 42 10.7 1.36 1.36
"USW00013893" 10-Jan-2022 0.05 41.9 10.7 1.5 1.5
"USW00013893" 11-Jan-2022 0.05 41.8 10.7 1.64 1.64
"USW00013893" 12-Jan-2022 0.05 41.8 10.7 1.77 1.77
"USW00013893" 13-Jan-2022 0.05 41.7 10.7 1.9 1.9
"USW00013893" 14-Jan-2022 0.05 41.7 10.7 2.03 2.03
"USW00013893" 15-Jan-2022 0.05 41.7 10.6 2.15 2.15
"USW00013893" 16-Jan-2022 0.04 41.6 10.6 2.27 2.27