Geez.
I hope you wash so frequently that you scrub some skin off.
Nothing in the Federal Register regarding safety of specific compounds delves into the area of mixing pesticides (I say pesticides in general terms). Complicated research goes into toxicity studies that for the most part extropolate animal data into human tolerances. Most of what industry is concerned about however, is quantifying effectiveness for the designed purpose, the health effects come later and only when it has to.
Many chemical families do NOT mix, have shorter half-lives than others, synergistic effects occur when mixing reproductive inhibitors with outright toxins or growth regulators. I can go out to my garage and create a bomb with the simple mixing of two nutritional compounds and adding a third common element to detonate at a designed time, using only a mixer or a glass insert barrier to trigger the outcome. I can't believe a nurseryman would do what you're saying but I do believe they could - business is business I guess. What he thinks is that he's used it this way so far with tolerable plant mortalities so I guess he'll remain doing this.
I would add though, that label restrictions prohibit using these chemicals (in this case anti-fungals or fungistats) in this manner and he's directly violating Federal Use Standards and laws. Perhaps the local enforcement authorities don't give a rat's ass about this practice but I know of many Feds that would love to know more. It's your life, and I know employment is a necessary evil, but there may be some dire chronic effects over a period or years ahead so you may at least want to document the practice with dates, methods, verbal directives from him, and labels from the chemical themselves. Save this stuff for future reference, trust me on this. I was diagnosed terminal with lymphoma in '93 and we paper trailed the exposures with known science and it pointed to the smoking gun held by the US Forest Service, who knowingly falsified data regarding warnings and use laws.