I submitted my resume online yesterday, but I replied today, asking for an interview tomorrow. But I didn't say when. Do you need to call?

Call to explain who you are and what position you are applying for, say that someone invited you for an interview, but didn't inform you of the interview time, and then ask if you have any special information to bring to the interview. If another company asks you to agree to an interview tomorrow, you can discuss other interview times with him. No company only arranges a one-day interview.