Welcome to the real world.
At this point you can lookup the specs for ESR of your electrolytic caps and see how that compares to the output impedance of the port driving that capacitor.
(Both)
The IC spec says Low Output Impedance 28 OhmTyp
TC962 can source as much as 80 mA but I do not recall a graph of ripple vs current.
You can lower the ESR of the Caps,
define your noise spec mV-pp, see if signal supply noise rejection is adequate, and consider LC Filter if you need more ripple reduction.
Also be sure your probe ground leads use 1~2" clips or use coax.
Be careful of layout EMI... Isolation, CM Filtering, Shielding, ground, supply ESR, ESL
B.T.W. so called General Purpose 10uF caps have ESR around 30 Ohms in SMD and 15 Ohms in Radial
and so-called low ESR Caps will be < 1 Ohm for this value in 25V