Tamiyo's safekeeping
Tamiyo's Safekeeping isn't consistently having the indestructible effect. The game also doesn't always allow a response after blocker declaration or after spell casts during which time it could be cast as it's an instant. After reading through bug reports here, it's proving to be a consistent issue across the board. I am currently playing on android. In my particular situation I had cast Tamiyo's Safekeeping in response to an ETB proc which would give my newly summoned monk token a -1/-1 until end of turn. The spell wasn't countered however the token still was destroyed. This is the second occurence; I assumed the first time was a fluke. I hope that was enough information. There weren't any relevant screen shots to take after the fact.
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Rezzahan#77802 commented
Your creature died because it had 0 toughness, it wasn't destroyed. These are two different state based actions, the first simply puts the creature into the graveyard, the other destroys. Tamiyo's Safekeeping helps only against the later. Hexproof can help against targeted -X/-X effects, but I assume the -1/-1 in your example came from an untargeted source.