Does the term "Alkaline" necessarily indicate the presence of an actual alkali?
Most every English language dictionary definition of alkaline that I've found defines it as the adjective form of alkali and includes something like "having a pH greater than 7".  As pointed out in the comments there is no IUPAC definition, so it's going to be difficult to come up with an authoritative scientific answer.  Here are some interesting items I've found on the word's origin, usage in different contexts, etc.:  

Online Enemology Dictionary:
alkali: late 14c., "soda ash," from Medieval Latin alkali, from Arabic al-qaliy "the ashes, burnt ashes" (of saltwort, which abounds in soda due to growing in alkaline soils), from qala "to roast in a pan." Later extended to similar substances, natural or manufactured. The modern chemistry sense is from 1813.  

Cambridge Dictionary :
alkali: chemistry - a substance that has the opposite effect or chemical behavior of an acid. adj. alkaline  

Biology Online: 
alkaline: (Science: chemistry) Having the reactions of an alkali. Origin: L. Alkalinus Relating to or containing an alkali; having a ph greater than 7; alkaline soils derived from chalk or limestone.A substance that has a ph higher than 7.  

Merriam-Webster:
alkaline: :  of, relating to, containing, or having the properties of an alkali or alkali metal :  basic; especially, of a solution :  having a pH of more than 7   

The almighty Wikipedia, fairly representative of a half-dozen other online definitions:
In chemistry, an alkali (/ˈælkəlaɪ/; from Arabic: al-qaly القلي, القالي , “ashes of the saltwort”) is a basic, ionic salt of an alkali metal or alkaline earth metal chemical element. An alkali also can be defined as a base that dissolves in water. A solution of a soluble base has a pH greater than 7.0. The adjective alkaline is commonly, and alkalescent less often, used in English as a synonym for basic, especially for bases soluble in water. This broad use of the term is likely to have come about because alkalis were the first bases known to obey the Arrhenius definition of a base, and they are still among the most common bases.  

I think in the end its usage is simply tied to the jargon and vocabulary of the context in which it is used. And with so many definitions, most of the ways that we hear it used are probably at least partially correct.  And as is so often the case, I think the Wikipedia definition probably comes as close to the best definition as any.