Yes it would stack. And yes, untyped bonuses like that should never be a thing.
Point them to the War Master that's also on that site. It's much better designed, IMO.
Also, flagged to be moved to compatible products.
The Tome of Secrets isn't generally known for its balance.
WotC :p
Let me second Cheepy's suggestion you instead use the war master (found here) over the warlord. It's better written, more interesting, and less likely to cause problems in a campaign. I also recommend you pick it up as the very-reasonably-priced pdf (here). because A: It has more masterwork equipment (good for the mark of quality ability) and B: Super Genius games deserves to make a buck on it. ;D
As for what companies to look out for, I find Super Genius Games {here)and Jon Brazer Enterprises (here) are the two I trust to be as good or better than Paizo. Several others (Dreamscarred Press, Open Design, and Rite Publishing ion particular) are pretty good, but you have to watch out for questionable writing or unbalanced rules in some books.
Of course I am also more cautious about Ultimate Combat and Ultimate Magic than I used to be, and they're by Paizo.
As for the warlord b0onuses stacking, the rule is "Bonuses without a type always stack, unless they are from the same source." So you'd have to have a GM decide, is two uses of the same ability from two different characters the "same source" or not. Most GMs agree it's not (though two uses from the same character would be), but it's not entirely clear in the RAW.