There’s different levels as I understand. There’s really pure DI for chemistry labs, reactors, high voltage electronics, etc., and then there are grades that have some higher level of pass-through.
IIRC, true DI will show no conductivity, but it will start to absorb CO2 from the atmosphere and begin to show conductivity in time.
Lifelong chemist, and in a previous job "babysitting" our house DI system was one of my duties.
Basically it had been installed several years prior, and Culligan maintained it. It supplied labs on 4 floors of a large building, and by my calculations had about 2 miles of piping through the building. The resin beds, pump, etc were by one of my lab workspace, and I'd often have to chase down air bubbles on the top floor of the building.
Ours fed regulated pressure tap water in, which was then circulated through two cation/anion exchange mixed bed resins and a charcoal filter. Each of these was about the of a 300cf gas cylinder. We also had a particulate filter and a UVC germ unit. When Culligan came(we had to call them, but it was every 4-6 weeks) they would replace the particulate filter, the charcoal tank, rotate one of the mixed beds to a different position, and then exchange the other mixed bed.
Our system had a guaranteed resistivity of 1MΩ/cm. In the middle of all of the above was a little neon light that would light when the resistivity was this or better, and would go out when it fell below 1MΩ/cm. I'd check it every day, and call when it went out. They'd usually come in 2-3 days. There were a few times I was out on vacation and the person supposed to check didn't, and it would go for a week or two-sometimes that would require that the service change both the mixed beds.
My graduate work was in surface chemistry, which required high purity water. We had a Barnstead Nanopure system in our lab, which took the house DI water and used additional exchange resins along with charcoal filtering to lower down to what was stated as 18MΩ/cm. There was also a .5 micron final filter on the dispenser. I'll mention that I was in charge of maintaining that system when I was in graduate school, and with every cartridge change I'd let dilute bleach(no cartridges installed) circulate through the system for an hour or so-that was something that the trained service guys would do when they'd come in, and I figured there was no point in paying them for something I could do myself

. People would often get upset because immediately after service, the system wouldn't actually reach 18MΩ, but usually more in the high 16MΩ range(it had a display on the front telling you this). What one service guy told me was that it was a very rare system that could actually get that low(which IIRC is the theoretical conductivity of pure water due to auto-ionization at 25ºC), but that bacteria would build up on the conductivity flow cell and give a false reading. The bleaching procedure would cause the system to give a "true" reading for a while, and poeple were generally more content to have the false 18MΩ reading

(never mind that when I'd use an external conductivity probe before and after service, the "16MΩ" water would actually read better than what had previously been indicated as 18MΩ).