Exactly, it puts me to sleep 4-6hrs later. I was discussing it with a company owner, and he said 'impossible, that's not how it works'. Lol, ok bro. I know many people who have the same reaction.
He's saying it's not possible for theanine to reduce the perceived energy you get from caffeine, or it's not possible for it to make you sleepy? Theanine is, for the most part, calming but not sedating, but if you're taking it with caffeine, you'll likely get some sort of comedown from even just the caffeine alone eventually, so it's not out of the question that you'd feel a bit more tired 4-6 hours later if you have too much theanine with your caffeine, as it balances/calms the energy from the caffeine from the outset. I like adding ornithine HCL to my caffeine, since it's been shown to potentiate the effects/duration of caffeine at 8 hours post-dose, which I find means longer-lasting effects and less crash/comedown.
Anyway, the research pairing caffeine with theanine tends not to use a very high dose of either, with this one using 250mg caffeine and 200mg theanine being probably the highest dose of either that's been used IIRC, and found that:
Caffeine increased self-rated alertness and jitteriness and blood pressure. Theanine antagonised the effect of caffeine on blood pressure but did not significantly affect jitteriness, alertness or other aspects of mood. Theanine also slowed overall reaction time on the visual probe task.
https://www.ncbi.nlm.nih.gov/pubmed/17891480
As to 350mg theanine, well, you're almost doubling the dose of what was used in this study, which I see no reason to do.
Then there's this study, which used coffee and tea, so isn't exactly the same, but it found that:
During the acute phase of beverage ingestion, caffeine significantly sustained performance compared to water after the first beverage for CFF and subjective sedation (P<0.05), and after the second beverage for the Recognition component of the CRT task (P<0.05). Additionally, there were significant differences between tea and coffee at 75 mg caffeine after the first drink. Compared to coffee, tea produced a significant increase in CFF threshold between 30 and 90 min post-consumption (P<0.01). However, following the second beverage caffeinated coffee at 75 mg significantly improved reaction time (P<0.05), compared to tea at the same dose, for the Recognition component of the CRT task.
https://www.ncbi.nlm.nih.gov/pubmed/10823400
Now, I may well be wrong, but perhaps the higher dose of theanine that people ended up consuming once they had their second serving of tea may have been something of what you're describing, with higher doses of theanine once you have multiple servings of tea?
Personally, I prefer ~100mg theanine in the context of a PWO, and no more than 200mg theanine in the context of a general energy or work/study aid style supplement. 350-400mg acutely is more for relaxation, or to be taken in the evening/night IMO. The only potential exception is if you're using a TON of stimulants and really want to try to balance it out, but even then, 350-400mg still seems like a lot in the context of a PWO IMO.
Edit: more info:
This potential chronic regulation of levels of alertness and performance of simple tasks afforded by tea consumption is consistent with the neurochemical effects of L-theanine and the interaction between L-theanine and caffeine. The effects of L-theanine on neurotransmitters suggest it has a regulatory role in brain function, modulating excitatory brain responses. Furthermore, L-theanine appears to antagonize the stimulatory effects of caffeine on the brain. This is supported by the few studies that have investigated the effects of L-theanine, in conjunction and in comparison with caffeine, on cognitive performance. These studies suggest an interactive effect of these two dietary components of tea. L-theanine appears to enhance the effects of caffeine on speed and accuracy of information processing, mental fatigue and tiredness, and, importantly, on more complex tasks such as sentence verification, word recognition, the speed and accuracy of sustained attention, and the ability to ignore distraction. These tasks may be more reflective of the cognitive performance required in stressful, everyday occupations than the simple speed of perception and speed of reaction tasks used in the caffeine-only research.
Importantly, L-theanine may also work in combination with caffeine to enhance performance of more complex tasks, such as attention switching and the ability to ignore distraction, which may be reflective of higher-level cognitive activity, such as the executive functions, and which may be sensitive to the detrimental effects of overstimulation on cognitive performance.
It's possible that people may like the "overstimulated" feeling of higher doses of caffeine in the context of a pre-workout supplement. Or just that more moderate doses of theanine can still provide the balanced/focused energy and synergy without taking too much of the "edge" off of the caffeine in the context of pre-workout use.
https://www.ncbi.nlm.nih.gov/pubmed/18254874