Green’s Dictionary of Slang

tumble v.2

[fig. uses of SE tumble on, chance on]

1. [mid-19C+] to realize, to notice, to recognize; thus tumble to

2. [mid-19C+] to agree (to), to take a liking (to).

3. [mid-19C+] (UK Und.) to understand.

4. [mid-19C+] (UK Und.) to alert, to make someone suspicious.

5. [20C+] (US Und.) to be arrested.

6. to listen.

7. [1950s+] to unmask, to recognize as fake.

In phrases

tumble to (v.)

1. [mid–late 19C] to involve oneself energetically or enthusiastically.

2. [mid-19C+] (US) to discover, to become aware of.