msumm21 said:

TL;DR: Wondering how the early experimenters came to certain conclusions

I have a question about JJ Thomson’s cathode ray experiment evidencing electric charge in an atom.

A DC power source was used to create voltage, evidently some kind of battery.

So, at the time of the experiment, they could make DC power sources, but did not know those caused charge to flow in a circuit? If not, did they have a working theory for what power sources were doing?

Given this background, how did they know the “stuff” traveling through the tube came from the atoms in the cathode? They knew the power source well enough to know that it didn’t “create” this stuff internally and circulate it through the circuit?

It seems that they did know that charge flowed in a circuit. Thompson himself tries to measure charge by the time it takes to accumulate on a capacitor. When they experimented with electricity passing through gases, Thompson supposed that charge was being carried by corpusles, but it was not known whether + or - charges were involved.

In Thompson's case his tube contained a little gas, and he found that the charged corpuscles were coming from the gas, not the cathode. He found that with a positive anode in the tube, the corpuscles carrying the charge were attracted to the anode and so were negative. In a classroom experiment of a tube with a hole in the cathode, we can also detect corpuscles emerging from behind the cathode, and these are positive ones (positive ions - heavy charged atoms).

Thompson's paper can be read at this URL. http://dx.doi.org/10.1080/14786449708621070
He did many experiments to find out the charge and velocity and whether the particles differed depending on the gas used or the metal from which the electrodes were made, but concluded that the particles were always the same, having very small mass and large charge.

The power source used by Thompson was an induction coil, or transformer, with a low voltage primary circuit using a vibrating contact. From Faraday's work, they knew the polarity of the high voltage produced.

I feel this is not sufficent information to answer you but maybe a start.