If you’ve blocked someone on Twitter they can still see your tweets.
They can always see them by logging out (unless your account is also private) but all of the third party apps I’ve tested will also let them see your tweets while still logged in. Official Twitter apps (Twitter for Android, Twitter for iPhone) don’t seem to and if they look at your profile they’d find they can’t. now seem to let you see all their tweets in search results (and you can reply to them) though they still don’t let you see their profile.
If you have access to more than one Twitter app and someone has blocked you then you can find out what you can see of their tweets by using the testing script below.
Type from:username into the search bar. If they’ve made their account private you’ll probably see nothing, but on most of the apps I’ve tested this with their tweets will show up.
Re-run the search while logged out.
Type to:username into search – this will show you all tweets sent to a person, from which you can probably infer a fair bit of any conversation they’ve been having.