After progressing a bit in the demo talking to certain NPC's will tell you to talk to them at a later date for example talk to the person near the Poke Center after a day and receive an item. There are also a few more. Maybe there are items transferable to the full game.

 

Did you change the system time?

 

I was't going to, I learned from Yo Kai Watch 2. I was just wondering how you knew.

 

Which person will progress the "story" the guy near the Poke Center says he will just give an item.

 

Which?

 

the real secret is what that vending machine is selling for 1 million!

however there is a lady that said in 5 days someone will appear, not sire if 5 days in real time or 5 days that i played the game... we will see...

 

but the game will be out in november...

she really says that in 5 days there will be someone to visit her that i should see him

 

The 18 days is the police officer telling you that something will happen.

 

Nothing really secret is going to happen on these days.
I made some text dumps and the only important thing is Ash Greninja.

Here the text in spoiler tags:

Sendable items:

Warning: Spoilers inside!

What are you sending to the full version?
- Greninja
- Stardust
- Star Piece
- Nugget
- Pretty Wing
- Balm Mushroom
- Comet Shard

Warning!
This Pokémon will not listen to what you tell it
until you have completed two grand trials in
Pokémon Sun or Pokémon Moon.

19th October event:

Warning: Spoilers inside!

If you come see me tomorrow, I’ll give you
something good.
Not today, not the day after tomorrow.
It’s gotta be tomorrow—got it?
You came! Thanks! Here’s the good stuff I
promised you!

Pikachu’s birthday:

Warning: Spoilers inside!

Guess how many days until my sweet li’l
Pikachu’s birthday? Just [VAR NUM2(0000)]!
Pikachu!
I wonder if someone will help me celebrate.
Believe it or not, today is my sweet li’l
Pikachu’s birthday!
Chu!
Would you help me celebrate?
Too bad...
Oh! I’m so happy! Happy birthday, my sweet
li’l Pikachu!
Pikachu-chu!
Thanks for helping us celebrate! Let me share
some of the fun with you.
We’ve both gotten another year older, my sweet
li’l Pikachu.
Pika-pika-pika!

Police Event:

Warning: Spoilers inside!

According to my informants, there’s a shady
deal going down right here in a matter of
days—[VAR NUM2(0000)], to be exact.
I wonder if I’ll be able to handle it by myself...
You! I’ve been waiting for you!
According to my informants, there’s a shady
deal going down right here today.
I was worried all by myself, but if you’re here
with me, we might be able to stop this deal from
going down!
Shh! Someone’s coming!
You haven’t been followed, have you?
Hah hah hah... Hurry up and give me the stuff!
Oh...
*gulp*
Just what kind of a shady deal is this...
Slo?
Slo-slow?
Whoa! Some people will pay a high price for
Slowpoke Tails, and I’ve heard about them being
peddled around here!
I guess they’re trying to sell Slowpoke Tails on
the black market...
Ooh, your Slowpoke’s tail...
It’s so cute and tender looking! I just love it!
Ha ha ha... Your Slowpoke is also
super-duper cute.
Poke?
Oooohhh, it’s just too cute!
...
Well, that certainly was shady in its own
special way...
There’s a lot going on in the world that I don’t
need to know about...

Boat Event:

Warning: Spoilers inside!

I have to sail away on a ship in [VAR NUM2(0000)] day[VAR NUMBRNCH (0, "", "s")].
I’m afraid of boats, though, so I’m a bit nervous.
I hope you’ll come see me off on my journey.
Sure!
I don’t know...
I’m so happy! It’s a promise—see you here
in [VAR NUM2(0000)] day[VAR NUMBRNCH (0, "", "s")]!
Oh, I see... I get it...
I have to sail away on a ship today.
I’m afraid of boats, though, so I’m a bit nervous.
I hope you’ll see me off on my journey.
Of course!
Ummm...
I see... Too bad...
I’m so happy! Thank you!
I’m scared...
But since you’re here, I think I can do it!
Let me give you something to show you how
thankful I am.
At last I can see my mom and dad again!
Good-bye...

 

Here's footage of the twenty four day ferry event.