It seems that the person who instructed you this way regarding the berakhah on the ner havdalah was simply mistaken.
While there is an opinion that on ^erev shabbath one should first light, then cover their eyes and recite the blessing, and then uncover their eyes to see the light, there is no such custom or opinion anywhere with regard to doing so at havdalah at all. And - le-^aniyuth da^ati - even on ^erev shabbath it is more correct to recite the berakhah for lighting and then to light afterwards [cf. Hilkhoth Shabbath 5:1].
It is clear according to all, however, that the berakhah of borei me'orei ha-esh is fundamentally different from the berakhah of le-hadliq her shel shabbath in that the former is on the actual lighting of the lamp while the later is on the light itself. Thus, the Rambam writes in the Mishneh Thorah, Hilkhoth Shabbath 29:25,
"[At havdalah] we do not pronounce the blessing on the lamp until
we benefit from its light to the point that [the light is bright
enough that] it is possible to distinguish between coins of various
[See Hilkhoth Shabbath 29:24-29 for a complete set of instructions and regulations regarding the essential miSwah and elements of seder ha-havdalah]
As you correctly noted in your question, this language certainly not only implies but requires that the havdalah lamp be lit before reciting the berakhah of bore me'orei ha-esh. Most commonly, in order to specifically benefit from the light, people are accustomed to "inspect" their fingers and fingernails in the light or to read from a book/siddur during havdalah. [Making a berakhah on the candle while your electric lights are on is almost certainly a berakhah le-vaTalah (a blessing said in vain)!]
One last note. As someone who routinely interacts with and answers questions from those who are either new Jews or newly religious Jews, I can tell you that it is extremely important to always seek the guidance of a competent Rav in any halakhic matter. If one has a friend who is knowledgable in a certain area, then one may rely on that as well (i.e. ^aseh lekha rag, uqneh lekha Haver - "appoint for yourself a Rav, and acquire for yourself a knowledgeable scholar/friend). Confusion abounds from well-meaning Hebrew school teachers and mikveh ladies who feel that they are "rebbetzins." To avoid such confusion, always ask a competent person who is adequately knowledgable in the dictates and principles of the halakhah.
Hope this helps. Kol tuv.