Tertiary alkyl halides can also undergo E2 with a strong base. Tertiary alkyl halide doesn't necessarily prefer substitution or elimination. Sometimes you get a mixture. You must consider other reagents to determine which pathway is more likely.
How to avoid mixes:
sn1: weakly basic nucleophiles (water, alcohol)
e1: non-nucleophilic bases: choose an acid with a weakly nucleophilic counterion [H2SO4, TsOH, or H3PO4], and heat.