My initial insight is the difference between the ph and alkalinity numbers between your tests and the pool company's tests. That's quite a difference. But don't assume your tests are wrong. Most pool companies now use a digital analyzer instead of testing the water with liquid drop reagents. If that's what the pool company used and the tests you did were with liquid drop reagents, I would trust your numbers.
Your ph number shows the ph in the acceptable maximum range. Their numbers show a high ph.
Your numbers show total alkalinity in the ideal range. Their numbers show an alkalinity level that is too high.
Their calcium hardness numbers show a bare minimum level of CH. This will need to be addressed before you turn the SWG on and brought to a minimum of 350 ppm.
The CYA level, if it is correct, is within the acceptable maximum range. So you need to keep an eye on that.
For the chlorine, their numbers show that the combined chlorine in the water is below .5 ppm. So if their numbers are correct you don't have any organics in the pool that would require super chlorination or shocking.
But you do need to get chlorine in the pool before nasties start to grow.
For a pool with a SWG and 85 ppm of stabilizer the chlorine level should be maintained at a level of 4 - 6 ppm.
So I would have the pool guy add 5 ppm of chlorine to the pool tomorrow (Tuesday). And unless he's gonna come back every day until you turn the SWG on, you will need to maintain that 5 ppm level on the days he isn't there.
One last point of information that you may not be aware of: A SWG requires that pool chemicals are adjusted so the water is brought into balance before the generator is first turned on. There is a recommended order for doing this.
1. Adjust the salt level. Most SWG mfgrs recommended range is 3000 to 3200 ppm. But some mfgrs require a higher level so check the manual. It's also a good idea to add an additional 200 - 400 ppm to the mfgrs suggested salt level because the salt level tends to drop over time.
2. Adjust the CYA to between 70 - 80 ppm. You're already there, just hav the pool guy check the numbers (assuming he has a test kit that will do this)
3. Adjust the Total Alkalinity to 70 - 80 ppm. This is IMPORTANT! So have to pool guy verify the pool company's number with his kit and adjust as needed.
4. Adjust the PH to 7.2 to 7.8. This is also IMPORTANT!
5. Adjust the Calcium Hardness level to 350 ppm
After the SWG is turned on, adjust the SWG percentage or pump run time so the Free Chlorine level stays between 4 and 6 ppm.