It should work out fine.
Not to be negative...however...if you read about Turnberry between the lines at the grower's website, it says something like "a fine texture, medium green turf-type tall fescue..." To me that means "light green"--and run of the mill quality. "Mixes well" probably indicates that it needs improved quality types to produce top-quality turf. What is the percent Turnberry in the blend?
All the other types are listed as " dark green", "disease resistant" "elite", "heat tolerant", "drought tolerant", "spreading type", "high in endophytes for insect resistance" or "very high-quality". They all have product sheets--Turnberry has none. Turnberry may be an older type, as it is mentioned in 2004.
Is it fresh seed? At what date was the seed last tested? 6 months is OK--over a year--not so much.
The usual seeding rate is 6 to 10 pounds per thousand sqft. September is a better time to overseed. Why are you overseeding? Improve color? Density? Bare spots and drought injury? Shade? Disease? Insect damage? Is the site irrigated?
Give or take...the best time to seed in spring is about the time of the first mowing.
If your lawn has mostly elite types already, then you don't want to take a chance of getting patches of a lighter green cultivar.
Was it originally sod, (if so, it is probably a dark green type).