Technicality with the wording of a couple of my "Aztec" monsters

[Quzo]

I'm currently making an Aztec archetype as you will have guessed. Like their real world counterparts they are based around sacrifice and become more powerful the more monsters you control are Tributed. They are based around summoning their trump card "Huitzilopochtli – The Sun" and gaining Tributes for his effect.
I have a question about the wording on a couple these cards; and my question would be that by the way I've worded these would their secondary effects activate if a monster is Tributed by the effect of another card?
So this is how I've worded them:

(Aztec Warriors are a sub-archetype of Aztecs)

Aztec Warrior - Eagle ATK/1700 DEF/400 WIND/Warrior Level 4

If this card destroys an opponent's monster by battle, Special Summon 1 "Slave Token" to your side of the field (ATK 0/DEF 200) with the same original Level, Type and Attribute in face-up attack or defense position. It cannot declare an attack or be used as Material Monster. By Tributing 1 monster on your side of the field, this card can attack directly this turn.

Aztec Warrior - Jaguar ATK/1700 DEF/400 EARTH/Warrior Level 4


If this destroys an opponent’s by battle, Special Summon 1 "Slave Token" to your side of the field (ATK 0/DEF 200) with the same original Level, Type and Attribute in face-up attack or defense position. It cannot declare an attack or be used as Material Monster. You can Tribute 1 monster you control to have this card gain 700 ATK and DEF until the End Phase of your next turn.

[s]Basically, I want to make it so they have to Tribute monsters for their own effect rather than have people activate them when other cards are Tributed. Would have to change that to "By Tributing a monster..." or "You can Tribute a monster..." You can comment on the actual effects too if you'd like but this is mainly about the wording of those effects.[/s]
Wording of the Token issue, maybe?

EDIT: This card's text probably needs fixing (see italics):

Aztec Warrior - Cuahchicqueh 5 level stars LIGHT 2250 ATK 1500 DEF.


Cannot be Special Summoned from the deck. If you control a face-up "Pyramid of the Sun" you can Special Summon this card from your hand. If this card removes an opponents monster from the field by battle, Special Summon 1 "Slave Token" to your side of the field (ATK 0/DEF 200) with the same original Level, Type and Attribute in face-up attack or defense position. If you Tribute 1 monster you control this monster [i]can attack twice during the same Battle Phase[/i].

Do does that text mean it only gains the effect for one Battle Phase or as long as it remains face-up on the field? Because I only want it once so they have to Tribute another monster next turn to make it more balanced.

Was going to show my subscribers on YouTube once the archetype finished so if you're interested PM me. Although I'll probably post them here too.

[Bringerofcake]

The way you've worded them is fine. What's more the issue here is your use of "If this card removes an opponents monster from the field by battle..." As far as I can tell, battle is always destruction, and as long as you don't specify the graveyard, it can work on monsters being banished as well. If you want to keep the original text idea, at least change it to "leaves the field via battle".

[Quzo]

Well I was thinking in terms of equip cards and card effects when I put that but I guess you're right. I was also wondering about the wording that summons a token. It does seem a little odd but as far as I know it's ok.