You get Echoes if there’s something you can purchase from Mother that you don’t already own. Essences are unlocked for purchase if you either own that essence directly at rank 3+ on any other character on your account, or if any character on your account (including the current one) has unlocked an essence from that same group (ie. source, groupings can be found in this blue post). You can only purchase an essence if it is unlocked via the above, and the current character does not have that essence at rank 3+, and the essence is for a role that character can perform.
For any character except pure DPS, if they unlock a rank 3 for one role from any of the groups in the above link, they’ll immediately start seeing Echoes drop, because they won’t yet have gotten the rank 3 from that same source for the other roles they can perform. For example, if a paladin unlocks Breath of the Dying Rank 3 from the new 8.3 rep, they’ll start receiving Echoes, as they can now purchase both Touch of the Everlasting (tanking) and Spirit of Preservation (healing) using those Echoes, since both of those also come from the 8.3 rep.
However, if a Hunter unlocks rank 3 Breath of the Dying (and has no other rank 3’s unlocked on his/her account), they will not receive Echoes, as both of the other two essences from the 8.3 rep are ones hunters cannot use, as they can neither heal nor tank. They cannot purchase anything from MOTHER as a result, and thus, no Echo drops.
So if your main is a pure DPS and none of your alts have any rank 3’s that your main lacks, your main will not receive Echoes. Same if your main is not a pure DPS, but has all of the tanking and/or healing essences at rank 3 from the same sources as you have DPS essences at rank 3.
So, you may not be receiving Echoes on your main because it is a pure DPS (just an inference), and your friend would be receiving them because they are not a pure DPS, so their rank 3 has unlocked the 1 or 2 other rank 3’s from that same source for purchase from MOTHER.
Unfortunately, this does mean that pure DPS mains will have a difficult time enabling Echo drops so they can save up while alts pursue various other Essences. That’s one of the major complaints about how Blizzard chose to implement this system, actually.