Both were "turning points" that doesn't mean May was the low and July the high. It would very well be that May is when it "turns" down and July is when it "turns" back up. In that sense it doesn't necessarily mean an absolute low or high - only when the trend is due to change.

We do. Armstrong says that it is based on Composite highs are where highs or lows are formed on intraday or closing highs.