Hi Grace, thanks for your reply. I have some follow-up questions though.

If I change the first sentence to: “4月20日是他母亲的生日。他当天就回老家去了。”Is 当天 now pronounced dàngtiān ?

I'm also confused by the second dictionary sentence:

票是当天的。　Piào shì dāngtiān de.　The ticket is for the same day.

当天 here means "the same day". Shouldn't this be dàngtiān (not dāngtiān)?