Alright before playstyle, some quick tips:
The pick only works, if you have either a competent mid or jgler, or a good botlane. If your jgler permafarms while being a gank champion, when enemy camps can be invaded or have blinkers steering them away from objectives even when the enemy jgler is dead. If either laners start inting with a 4-5 kill advantage while being the same level as the opponent. If the midlaner prefers dying over and over again, rather than rotating. If the botlane are not bad, but aren't good enough to carry their jgler who doesn't notice objectives, there is only so much you can do, other than /muteall for mental health.
Warn your teammates before hand, that top laner will get bounty which they will have to group to collect, and elsewise play the game as usual for their picks.
As a dbl jg, expect urself to always be starved of xp.
There are games, where my team was ahead 12 kills by 15 minutes, where I hadn't hit level 6 yet.
Keeping that in mind, lvls are free golld turned into stats, avoid 1v1s unless you are 100% you can kill them before they can land more than 1 ability on you.
It is alright to be full health, see the enemy jgler on 10% and only snipe a dark harvest stack, because the level discrepency usually means if they can reach you, they can outlast ur dmg and kill u. Only procede to go in, when you are sure their laners can't rotate in time, and they can't land more than one ability on you. Remember: Forcing their back, is better than losing a lot of hp for a kill, cuz it allows you to invade them and stay on the map ganking more.
Alright, I've been adapting my playstyle a bit after catching happy's twitch video, it gave me some insight on how the early game can be better played.
You have a general pattern, which you adapt when either their jgler has a lot of stick potential, their laners are capable of flash hard cc, if enemy top laner has built hullbreaker or is a hyperscaling champ.
Lvl 1, you rush to an enemy buff, if their mid laner is pokeable you can place a tracking ward and rush to mid to get some free mulah. If their midlaner is playing safe, and no one knows you're in their side, you can wait till about 1:00-1:10 to place a ward that will last enough so that you know when enemy is taking the buff.
if that is the first buff you can smite snipe the buff last second, else if mid laner is pokeable, snipe that mulah, else leash ur jgler for a faster clear.
Then you can play poke in mid, so that you can either get the enemy killed or make enemy lose all priority and some xp. If the warded buff was second, you can go try to snipe smite when you see the enemy jgler have at it.
With taliyah, it is normally a q lvl 1, but on that 1% you can go w lvl 1, to get a better smite snipe, or better lockdown/disengage during invade.
If you either lvl 1 w, or don't have the ability to pressure a lane lvl 1, soak xp and maybe gold in top lane until you hit level 3.
Otherwise you can be lvl 1 roaming for the first 5 minutes, provided you are being impactful.
If you have layed enough pressure, you should usually be free to take first scuttle, so that your team secures both scuttles.
W helps break scuttles shield and stuns it from movement for 0.5 seconds after landing.
Remember to go to any empty lane to soak xp, help wave management and last hit when the gold is being lost elsewise.
You can generally leave top to be, however if you can't apply pressure on map, it can be beneficial to secure top lane xp, while backing enemy top laner from taking plates/tower.
If your jgler is competent and you haven't inted the first five minutes of the game, you should be able to secure a dragon every five minutes.
If the enemy has a high stick jgler, you should avoid invading unless you see them elsewhere on the map.
If their laners can flash stun you, you can play away from that lane or play real far back just to land q pokes. Flash stun laners basically make you feed if you don't play it perfectly.
When top lane has hullbreaker, you plan to permagank top with either jgler, mid or both. If that's not possible, just shush them away from towers.
If the top lane hyperscales, I don't really have any advice, as the only hyperscale laners I've versed, were bad enough to lose freezes and therefore our minions die under our tower, we won the game before they could scaled up. Or mid and jgler handled top laner pretty well.
Your ult is extremely high impact, but too be honest ironically you aren't gonna need it that much. You either use ur ult to close escape paths during ganks, protect your teammates from an enemy attack, to suprise gank, to block enemy paths towards an objective.
Taliyah has a lot of usuage for her ult, it really depends on the situation. But the best way to use her ult, is to not allow enemies to exit their sanctuary while you emote and your single ranged minion kills the nexus for you.