Technically, Botanical Latin is a written language, not a spoken one. Technically, there is no right or wrong, but we need to understand each other, so it is good to try to have norms. These norms can differ in different parts of the world, too. Different norms have their roots in four (or more) rivaling speech patterns: ancient Roman, Church Latin, Latin spoken in northern continental Europe (think Linnaeus), English method (kind of more Anglicized form). You will hear things like: there is no soft "c" in Latin, a "v" is pronounced like an English "w" or there is no "w" sound in Latin. These and many more stem from the different Latin speech patterns. In addition, throw in the fact that much of Botanical Latin comes from the Greek language, and other languages, too, that are "latinized". It's on wonder that learners are confused.
Don't fret about it, but there does tend to be some more universal acceptances. The dipthong "ae" was actually pronounce like the "ai" in aisle in ancient Roman, but now it is most common pronounce as a long "e" as in bee. The seemingly uncomfortable way of saying Araceae (a-ray-see-ee) is from your own speech pattern that is foreign to Latin speech. Araceae is not an English word. Why does it need to sound like one? It doesn't. Again, don't fret. Self-centric linguistics is a natural tendency for all of us. It's really quite interesting to learn that there are a lot more sounds and patterns that are not represented in your native tongue. Force yourself to use these "weird" ways of speaking and eventually it will become normal to you. (And when the words just roll off your tongue, you'll impress your friends, too.
I don't think Bill is capitalizing the "e" to mean it is accented. I'm not sure what he is doing there, or what distinguishes his use of "ee" as opposed to "E". (Is it supposed to be a schwa "e" (ə)?) I am baffled. To be clear, there are no Latin variations to my knowledge that ever accents the last syllable. Except for when latinizing non-latin words (like someone's name), the major accent falls on the second or third to the last syllable.