You could try scaring them by dashing or simply walking forward if they’re running away. Adon has good footspeed and a very quick dash so walking them into a corner shouldn’t be a problem. Obviously the challenge is keeping them there. I have some ideas on taking advantage of the situation that may or may not be of use:
~Against turtling: correctly spaced JKs or aerial JKs of all ranges (chip), EX JK (overhead), f.mp (overhead), blockstrings that may or may not end with JK or a tick throw.
~Against neutral jump/jump back: EX JK (combo), correctly timed aerial (into sweep or combo if they land), wait
~Against jump forward: correctly spaced anti-airs (eg. st.mk, cr.hp, RJ, U2)
~Against Shoryus/mashing: bait and punish (simplest options are st.hp and st.hk, blockstring mixup, HK JK (possible trade or stuff)
~Against Air Tatsu: mind reading aerial (preferably mp or fp), or pursue with JT
~Against footsies and pokes: outfootsie them, or space your JKs
Also important: if you have a decent life lead, you have no reason to follow your opponent. If they insist on playing it lame, follow suit: you’ll win the time-out. They have to come to you, so of course be ready for them when they finally get wise to their disadvantage.
Adon has solid tools for dealing with scrubby fireballs. EX JK, JT (in moderation), U1 (personal favourite) FADC (fast dash ftw) and his narrow, quick jump arc should be a great help. Shoryus and mashing have more universal solution: bait and punish.