You have probably preceded the distillation under vacuum and after the end of distillation you have quickly open the air valve. Thus, atmospheric oxygen violently penetrated in the warm (hot ?) distillation flask and quickly oxidized the so prepared 2-methyl -1,3- dithiolane to a mixture of the corresponding 1-oxo- and 1,3 –dioxo derivatives.
(Remark: Serious fires might start by similar procedures, in bulk quantities ( > 1 ton). Why?).
Alternative procedure 1: Slowly opening the air valve after the end of the vacuum distillation.
Alternative procedure 2: After the end of the vacuum distillation, gradually increase the pressure by slowly introducing N2, at low rate and monitor the pressure by the manometer.
Alternative procedure 3: In acidic aqueous medium (TsOH), 2-methyl -1,3- dithiolane will be hydrolyzed and ring opening will occur. So, you can proceed the extraction with a saturated mixture of NaHCO3, followed by washings with water until neutral to litmus.
PS: Boiling point of 2-methyl -1,3- dithiolane 175 °C at 760 mmHg that roughly means near 70oC at 14 mmHg. (If you operated a distillation at normal pressure at ≈ 180oC, it is even worse, regarding sulfur oxidation.)