There is some mixing of the terms here.

Many others had small sags or just looks gross, so there was a mix of installing new drywall or sanding them down and all ended up with a knockdown finish.

Some institutions, such as mine, will loan off of appraisal value rather than purchase price after 6 months of seasoning, sometimes even less. 

The portfolio was a combination of Single-Family Homes, Duplexes, Triplexes, and one mixed-use building.

These have no seasoning period.   

If you are seasoned from a lot of flips you have the means (contractors, knowledge) to deal with about everything efficiently and deep enough pockets that you can afford to loose money on one deal. 

Do I need to season the money I pull out or is it ok for me to finance my down payment on next property that way

NOW HOLD UP . . . an important caveat I'll throw in here is that there is a key difference between tenant for a season and tenant for a reason folks. 

Amy,When you buy all cash and want cash back out ASAP you have delayed financing where you can pull out 75% for example and use the purchase price as the appraisal rather then waiting (6 months) for title seasoning. 

Banks want a track record, established, a high credit score, and seasoned investor.